LAURA ROBSON's career continues to travel in the right direction.

Not only did the 19-year-old win the affections of the Centre Court crowd as she booked a third-round berth for the third time in her last four slams with a composed 6-4, 6-1 victory against Mariana Duque-Marino of Colombia, but she also revealed afterwards that she has gained the support of One Direction duo Harry Styles and Liam Payne and consequently an extra 20,000 followers on Twitter.

Some of said boyband's most devoted fans are not so thrilled, however, judging by the way they jealously bombarded her with the Twitter equivalent of hate mail as to who exactly she was and how dare she have the temerity to receive personal messages from their heroes. "I haven't been really going on Twitter and, when I'm on court, I'm not worried about who's tweeting me," insisted Robson, who reluctantly admitted she was a bit of a fan of their brand of "cheesy music". "But I actually got an email from Twitter saying 'he [Harry] has followed you and messaged you'. I guess if you're that big-time, then Twitter gets involved.

"But I looked in my replies, and it was just thousands of these messages saying 'Who is she?'. I was wetting myself because it was so funny. I've gained 20,000 followers and they have no idea who I am. Then yesterday I tweeted, and it was hilarious, 'ps hi to the One Direction fans'. But they corrected me. 'We're not fans, we're Directioners.'"

Robson was certainly making friends and influencing people during her one hour 13 minutes under the roof yesterday. The Melbourne-born player might have won the girls' title here back in 2008, the first Brit to do so since Annabel Croft in 1984, but that was secured on Court No.1, as was this year's first-round upset of No.10 seed Maria Kirilenko. But unlike her opponent, a qualifier ranked No.117 in the world, she had previously graced Centre Court – in defeat against Jelena Jankovic last year, and then en route to her silver medal with Andy Murray in last summer's Olympic Games.

She said that remembering that fact helped her put a few first-set nerves behind her – she was a break down early on, then was broken when serving for the set at 5-4 – to record her first solo victory on the SW19 showpiece arena. "It is a big win for me," Robson said. "But then any match on Centre Court is a big one. Then I thought 'she is probably even more nervous than me.'"

Robson, whose lefty serve and topspin forehand in particular were functioning smoothly by the end, now faces Marina Erakovic – a grass-court specialist from Croatia who plays under the New Zealand flag – knowing victory would make her become the first British woman since Sam Smith in 1998 to reach the fourth round at the All England Club. Erakovic – Heather Watson's sometime doubles partner – eliminated the seeded Shuai Peng yesterday, and has a grass victory against Robson on her cv from last year. But she is only ranked 71 in the world to Robson's 38. Likewise, the 19-year-old is also regarded more highly than both of her two potential fourth-round opponents, Estonia's Kaia Kanepi and US wild card Alison Riske, making it plausible at least for her to become the first British women in the quarter-finals since Jo Durie in 1984.

However, the tag of being favourite is something she wore lightly yesterday. "I knew I was the favourite, and I thought I handled that well," said Robson, who was helped by the weather, which forced the postponement of her doubles match. "But Marina has pretty much a perfect game for grass. So I know it's going to be a tough one."

So emboldened was she after this one that she even articulated her ambition of winning the title one day, even if the brooding presence of Serena Williams – who Robson called the best player in tennis history – makes it unlikely to be this year. A bubbly Robson also joked about the wording of a question about potential semi-final opponent Serena "getting it on" with Andy Murray, and revealed her coach Miles MacLagan, who used to coach Murray, was introducing a system of favours and forfeits.

"The biggest dream is to win here pretty much," she said. "That's how it always has been. But on a day-to-day basis, Miles is introducing favours. So if you win the game, he has to do a favour or vice versa. So if there's a queue for the transport, he's got to line up, things like that. The other day I forgot my cutlery in the restaurant and he had to go get it for me."

Robson was watched by her dad and sister, but not her mother and brother. Mum Kathy has opted to stay in the family's new home in Greece with their two dogs – she praised her performance by text message – while her brother Nicholas is a court coverer and was otherwise employed out on Court No.18. She also downplayed her connection to Australia, the country of her own and both parents' birth. "My relatives still live there, that's about it," she said. "The only time I go there is for the Australian Open. They live in a very unpopulated part of Western Australia."

As it turned out, the One Direction crew were not the only publicity-hungry individuals desperate to make some political capital out of the situation. Prime Minister David Cameron had also been in touch.