What tickles me most about Judy Murray is this.

Around 20 years ago she was seen as a pest, a pesky "tennis enthusiast" who wanted to spread the word about her passion. Sports editors would dive under their desks when a minion shouted: "Hey, it's that Judy Murray on the phone. She wants you to publish the district tennis results." The various Jacks and Jims who held these editorial posts had an inbuilt dread of minority sports evangelists.

How times have changed. The girl who won 64 Scottish tennis titles, who took homebaking to her local club for an afternoon competition while selling French lingerie for a day job is now Britain's most famous sporting mother. Everyone wants a piece of Judy Murray as her son Andy continues to take global tennis by storm.

She says she no longer does interviews but reluctantly agrees to pick me up at Bridge of Allan railway station. The deal is we will have lunch and a blether about her life. As I disembark on a beautiful day I find Murray in her funky, colourful little car, patiently waiting with the engine purring. She looks tanned and healthy, an attractive 53-year-old who has been shaped by sport and the outdoors.

You cannot help but admire her authenticity. Murray has served her time. She has been an enthusiast, a coach of more than 30 years who would offer free lessons to children, the proviso being that the mothers of her young students would in turn agree to occupy her two wee boys, Andy and Jamie, in the park for an hour. Community life, its citizenry and values, has always been her priority.

"My parents were very sporty and community-orientated and it is a seed that is planted deep within me," she says. "My dad [Roy Erskine, a former professional footballer] was the optician in the town. My parents were both captains of the golf club, both champions of the tennis club and fundraisers. They instilled in me my sense of community, of belonging.

"My brother and I were regularly trekked down to the Dunblane tennis club, which in those days was four blaes courts and a little wooden pavilion. My mum was a Saturday morning coach, so I grew up with tennis.

"I was lucky – I had parents who played with me. We would hit balls against the wall of our house and every Saturday we'd be around the tennis club. You played anyone and everybody, and people brought sandwiches or pancakes or scones. I absolutely loved this scene."

Out of this emerged a small-town sporting hero – not Andy, but before him, his mother. With her feline features and willowy, sporty physique, Murray in the 1970s became Scotland's best tennis player (almost to a comical degree in terms of her dominance) and was ranked eighth best in Britain. In that lovely ambience which remains Scotland's small-town setting, where tennis competitions flourished, the sight of her turning up for tournaments with a racquet under her arm prompted regular comments along the lines of: "Here comes Judy Murray – she'll win."

"I think I won 64 Scottish titles, from junior level upwards," she says. "It sounds crazy, but in those days tennis was a tiny sport in Scotland – there were very few women playing competitively. It was a pretty small pool so it wasn't so difficult to become the best.

"In every tournament I was pretty much playing the same people. I'm sure other small sports in Scotland will tell you exactly the same. Sixty-four titles sounds pretty good, but in fact the level wasn't great."

For all this local tyranny, she never really got a bite at Wimbledon or the big time, despite one disastrous three-month period back in the mid-1970s when she gave the top tennis scene of Virginia Wade and Betty Stove a go.

"All I wanted to do was play tennis but there was nothing happening in Scotland, so I took off to play in tournaments overseas. I was 17 – fairly raw – and it was a very difficult thing to try to do. I was travelling on my own and I didn't know anybody.

"After a few months I was playing in a tournament in Barcelona and ran out of money. I had to get my parents to wire me money to a post office. I travelled on a bus to the post office to get the money, then travelled back on a crowded bus to the courts where the tournament was being played, and had my bag opened and pick-pocketed.

"I was standing on this pavement in Barcelona, 17 years old, looking and looking again in my bag for my money. I had to go to the police and then to the British Embassy. Finally, when I got back home, my dad said, 'Right Judy, enough – you're not doing this any more.'

"I've always remembered that Barcelona tournament. I played against Mariana Simionescu, who was Bjorn Borg's wife at the time. She was one of the top Romanian players. Back then, so long as you were half good, you just rolled up and played. I had no world ranking, it was just a different world. I think my desire to create opportunities for Scottish tennis kids was born of the fact there were no real opportunities for me in those days."

Today some say Murray's genetic prize has been the success of her two boys, Andy and Jamie, thus hoisting her into the glamorous world of professional sport. She is frequently spotted at the top tournaments as she watches Andy, the world No2. At the Australian Open in January her sense of fun and fooling on Twitter put her on a number of Sunday newspaper front pages.

But Murray sees it very differently. Her reward, she says, is not just the sons she had with ex-husband Will (they divorced when Andy was nine years old), but also a host of young tennis players whom she has coached over three decades either coming good or at least bettering themselves.

"My whole life was coaching kids – not just Andy and Jamie – and wanting to make them better. When I was appointed national coach in 1994 [by the Scottish Lawn Tennis Association] I identified about 16 kids, aged between eight and 11. Andy was one, there was Jamie, there was Elena Baltacha, Jamie Baker and others. I drove these kids here, there and everywhere for tournaments, including up and down to England.

"I still cry when I think of my first success as a coach. It was when I took the Dunblane High School boys to win the Scottish schools tennis championship in the early 1990s. One of those boys was Callum Davidson, the St Johnstone footballer.

"I was a volunteer at the Dunblane tennis club, I coached the juniors, I was the social convenor, then I was the club president. All I wanted to do was create an opportunity at grassroots level for Scottish."

Twenty years on, Judy Murray is no longer the sporadically unkempt, tracksuited tennis coach whose life is her children and her community. Instead she is a world-famous mother, a celebrity, a woman whose life is very different.

Image meant nothing to Murray in her age of innocence 25 years ago as she scurried about organising tennis lessons, her life an enjoyable yet unsung frenzy. But now – though she is loath to admit it – image has to matter.

"I've had to learn how to cope with the fame thing," she says. "As Andy's reputation grew around 2005, 2006 we were suddenly on an unfamiliar track – none of us had been down this road.

"All my life I hadn't just been interested in making Jamie and Andy better – I was looking after a whole bunch of kids. So it wasn't like I was a 'consumed parent', if you know what I mean. I wanted a whole bunch of these kids to get good at tennis – that was my goal."

The turning point for British tennis and the Murray family came in 2005, when Andy received a wild card for Wimbledon and reached the third round, where he lost to David Nalbandian.

"Wimbledon in 2005 – Andy's first big splash, so to speak – was our first understanding of the demands of the media and of us being in the spotlight. We had people following us home, we had paparazzi on our doorstep, we had TV and radio wanting our time.

"One paper wanted a picture of me loading a washing machine at Wimbledon for Andy. I duly did what I was told but I remember thinking, 'What the hell are you doing?' I had no clue back then."

Both Murrays had to get used to public exposure: Andy as the tennis player, Judy as the "celebrity mum". The pitfalls at times were painful. The younger Andy, with his instrinsically Scottish traits of wry humour and taciturnity, often attracted adverse comment. As for his mother – she of the tigerish encouraging of her son during games – some of the sports columnists became jackals when they turned their attentions in her direction.

"For a number of years Andy got a very bad press. As a young guy he struggled to handle that side of it. He was not loved – put it that way – by certain people in the media.

"I think there were quite a few writers who didn't get him. In 2005, when he was new on the professional scene, he was still a kid, trying to make his way in a very public arena. Andy would sometimes be pictured being petulant or bad-tempered, but that was only because he wanted to win.

"In the early days I would get nervous about doing interviews, but I often did things to save Andy from having to do more stuff. Then I got to a stage where I thought, 'You know what? Andy is old enough – he is doing all these press conferences now, he is perfectly capable of speaking for himself.'"

Meanwhile Murray had to adjust to her own place in the spotlight. In Melbourne, Paris, London and New York – the host cities of tennis's grand slams – the TV cameras forever pan round in her and Andy's girlfriend Kim Sears's direction. She has also borne the brunt of adverse public comment. "I've had it all," she says. "Quite a few people have written opinion pieces about me which haven't been particularly nice. I remember one which said I was 'the classic uber-tennis parent', the type who 'sharpens her elbows before she goes out to watch a match'.

"Well, you know what? I've always been sporty. I've always been competitive. I'm like Andy, or maybe he's like me – I wear my heart on my sleeve. And when something is great, then yep, I am right into it - I mean, 'Come on!' I sense the big moments, the big points.

"I've been through a spell when people wrote pretty bitchy articles about me. I kept having to say to myself, 'These people have never met me, they don't know me.' I guess the ones that disappointed me the most were by some ex-tennis players, who didn't know me or Andy from Adam.

"Boris Becker said at one point, 'Andy Murray won't win a grand slam until he ditches his mum.' I thought, 'What the heck are you talking about?' Or some psychologist would pop up and claim Andy was clearly traumatised by the mother figure, and wouldn't win a slam because he was clearly 'scared of failing in front of his mother'. I mean, really? Are you serious? What are you talking about?"

In recent years, Murray has accompanied her son to fewer tournaments but makes no apology for supporting her son. "The bottom line is: in a tough sport like tennis – almost a combat sport and for ten-and-a-half months of the year – you need a lot of emotional support because you are hardly ever at home, you hardly ever see your friends and family. For a guy like Andy, or any tennis player, there are some things that you can't discuss with your management or your coach – you need your family.

"What Andy is doing is incredibly tough. He's got a very high profile and it is important to have people around who know you. I really don't see why I should feel bad about being around for my son."

Speaking to her, I'm not sure Murray enjoys her fame. In professional tennis she is now public property, with every part of her appearance and character scrutinised. Deep down, I think the doyenne of the tennis scene in Dunblane once had a contentment that today is compromised.

"The coverage of my presence got much bigger after Andy won Olympic gold last year," she says. "He has now won a US Open, and I noticed people were shouting at me this year in New York when I was shopping on Fifth Avenue. People were shouting, 'Hey Mrs Murray! We love Andy!' and others were stopping me and asking for autographs. I'm thinking, 'Is this really happening to me, here on a street in New York?'

"There are ups and downs to it. You don't have the level of privacy you might want. I still have my own close circle of friends, but even then I sometimes have to be very careful what I say. I even think much more now about what I wear. I never used to think about that at all – I was one of those people happy to be in my tracksuit most days.

"There is, though, a huge bonus in living in a small community like the Dunblane area. You don't get much hassle. People know you from years and years ago. That's fine. It's lovely, actually."

She still enjoys a laugh and not least, to the acute embarrassment of her sons, in her public lusting after some of Andy's Adonis-like opponents. Feliciano Lopez, the Spanish player whom she has christened "Deliciano", is a particular favourite. Murray deliberately sends herself up in her public panting after Lopez, and it has caused laughter and a slightly earnest disapproval in equal measure. "That all started at Wimbledon one year when Andy was practising with Feliciano. Andy said, 'Mum! Mum! Come over and get your picture taken with Feli -' I said, 'No, no, it's all right.' Andy started saying, 'Feli, my mum fancies you rotten, she thinks you are gorgeous.' I was saying, 'Andy, shut up!' After that, it just became a running joke.

"I have a very good relationship with Feliciano but, of course, it got blown out of proportion. I have become good friends with Andrea Petkovic, who ended up playing mixed doubles with Feliciano. She tweeted me and said, 'Judy, would you like to coach us? We're prepared to give you 5% of our prize money plus your photo with Feliciano.'

"I replied, 'I'd rather have 5% of Deliciano plus a photo of your prize money.' That was it. You forget who is looking in on Twitter. But that exchange kicked it all off. It has been a lot of fun."

This fame, fun and publicity is all so different to how it was at the beginning. I take her back to the old days. In the 1980s she took a job as a rep selling French lingerie – "really classy upmarket stuff" – while frantically cramming in motherhood, coaching and much else.

"It's funny now when you look back," she says. "I wrote a local tennis column for what was then the Glasgow Herald. I used to write a gossip column for the Scottish tennis magazine of the time, which was a lot of fun. I sent Scottish tennis results to all sorts of papers. I just loved tennis, I was an enthusiast. I was just trying to get tennis out there, to raise the sport's profile."

Well, she achieved all of that, and more. n