Watching Cerrie Burnell push her daughter’s pram across the foyer of the swish Hoxton Hotel in east London, it’s hard to believe this is the same woman who has been accused of giving children nightmares.

Wearing a sundress, her long, wavy blonde hair hanging loose around her shoulders, Burnell’s enviably svelte figure attracts the admiring glances of a group of businessmen as she passes. Only as she draws closer do you notice the disability which had parents up and down the country flooding the BBC with complaints: her lack of a lower right arm.

Unhitching a baby changing bag from her shoulder, Burnell roots around inside, producing a blanket. She’s all set to feed 10-month-old daughter Amelie (“Don’t worry, I’m not breastfeeding,” she assures me with a grin), when her publicist leaps into the breach and offers to do it instead. “Are you sure? She’s a wriggler,” says Burnell, before gratefully flopping back in a chair and ordering pancakes from a passing waiter.

Fresh-faced and wholesome, Burnell has expressive blue eyes and a warm smile. Refreshingly for a television presenter, she is almost make-up free – “I did manage to put on some eyeliner this morning before Amelie started going crazy but gave up after that,” she admits – and I notice her gold sandals are from the very unstarry Clarks.

This year has been a whirlwind for Burnell. In fact, make that a full-scale hurricane. Eight months ago, in January, the 30-year-old was an unknown, rookie children’s television presenter about to make her debut fronting the CBeebies shows Bedtime Hour and Do And Discover. As a jobbing actress, Burnell’s on-screen exposure until that point had been limited to a few small parts in the likes of Grange Hill, The Bill, EastEnders and Holby City. And then she got the call from her agent to say she had landed the CBeebies presenting job – and with it a hefty foot in the door of the zany world of kids’ television. She felt like she had scored her big break.

But within hours of her first broadcast the negative comments began to stream in. Soon, the messageboards of the CBeebies website and that of the BBC’s online disability magazine Ouch! were flooded with postings about Burnell, some so derogatory and vicious they had to be immediately removed. Some parents complained that Burnell was “scaring” their children, with one father stating he planned to ban his daughter from watching the show because he feared it would give her nightmares. Another suggested things wouldn’t be so bad if Burnell would only pull down the arm of her cardigan to disguise the fact she was missing an arm.

Some expressed concerns at being forced to discuss difficult issues with their young children before they were ready. “My daughter won’t watch with the new presenter,” said one parent. “She is only two and notices the lady’s arm has gone. She thinks she is hurt.” Others suggested Burnell only got the job because of positive discrimination.

While the BBC received just nine formal complaints, the controversy saw Burnell catapulted into the public eye and sparked widespread debate. Disabled groups fiercely defended Burnell and the BBC’s decision to hire her. She also received messages of support from many parents who were outraged at her treatment. One blogger wrote: “I think it’s great the BBC have appointed Cerrie Burnell. The earlier children come into contact with disabilities, the better.”

Burnell herself admits to being caught off-guard by the swell of emotion her appointment created. “I was absolutely amazed to get the job so I think I was still in shock about that when it all happened,” she says. “Obviously, I am aware of the prejudices that exist, I have faced that throughout my whole career.”

She handled herself well during this period, coming across as a thoughtful, articulate and thoroughly unflappable young woman. “I am glad it happened,” she says today. “In one sense it is great because it has given me a platform and certainly established me in the public eye.” Burnell is sure this would have happened anyway, although it may have taken longer otherwise. “I’m happy because it has raised the profile of disabilities and made people think: ‘Why is there this massive hoo-ha over this girl with the strange arm?’”

Did she read the comments people had posted about her on the messageboards? “I didn’t, although when I first got the job I did have a look,” she says. “It just struck me as hardcore fans who like to write comments such as ‘I like those jeans’, ‘Where did she get that top?’ and ‘I’m not very keen on that T-shirt’. I know when Andy [Day, fellow CBeebies presenter] first got his job, someone wrote that he looked like a coke-head. That’s what you get in chatrooms – it’s how they work.”

When the notion of positive discrimination is raised, Burnell doesn’t flinch. “To be honest, when you go to an audition, you always hope that everything about you will help,” she says. “As an actress looking at a casting brief, if it said, ‘We want someone with one hand,’ I would think, ‘Yes, brilliant’, so whether that is positive discrimination or not doesn’t bother me. To me, it’s a way in.”

Burnell, it must be said, fits the archetypical image of the sunny, bubbly and super enthusiastic children’s television presenter yet somehow manages to avoid veering into the territory of twee. “It’s amazing, absolutely brilliant,” she says, her eyes wide and earnest. “It’s this crazy technicoloured dream world where you’re allowed to be really wacky with your imagination. It’s not too much of a jump from acting. Although you play yourself, you play the sunshine version of yourself. For children’s television, you need to be able to look foolish and not care.”

Does Burnell face any pressure from her bosses to maintain a squeaky clean image? “No, I don’t think so,” she says. “It’s just common sense. It’s not like my life has stopped or changed – it’s just I have more of an awareness that people perceive me as a role model. I mean, if I take my daughter to the park, I’m not going to stand there smoking. Not that I smoke anyway, but, you know ... after I’ve had a couple of gins I might be inclined to have a cigarette, but it’s not something I’m going to do in broad daylight.”

Asked about the burgeoning trend for children’s TV presenters to do adult glamour shoots (former Blue P eter presenters Zoe Salmon and Konnie Huq most recently joining a long line of alumni including Cat Deeley, Gail Porter, Caroline Flack and Angellica Bell) she bursts out laughing. “Oh my god, you haven’t seen the state of my tits after breastfeeding. I’m not going to do a lads’ mag shoot. That never would have been for me, even if I hadn’t had children. It’s not a route I would go down. It’s not something I would say no to in a film if it was what the role required, but I would have to feel it was necessary and not just gratuitous.”

The eldest of two children – her mother Carolyn is a dance teacher, her father Tony is a telecoms manager – Burnell grew up in Kent and spent her teenage years in Eastbourne, East Sussex. She was born without a right hand, the cause of which has never been medically established. For the first nine years of her life she wore a prosthetic limb and hated it. Then one day she simply stopped wearing it and felt liberated. Was she originally urged to wear the limb for cosmetic purposes? She frowns. “No, it was more they thought it would be an aid,” she says. “I found it a massive hindrance, so I stopped wearing it.”

She was, for the most part, unfazed by playground curiosity over her disability. Did her peers ever make fun of her? “Some did, some didn’t” she says breezily. Are children more accepting? “They get over it quicker but they are a lot more direct and will ask you more personal questions than an adult. I can certainly remember people saying stuff when I was younger. I wasn’t often hurt by it. I was 13 when I really became aware of what it meant in real terms to have one hand. Then I reflected on some things people had said to me, but it was only a fleeting phase – it wasn’t something I really dwelled on. I just became more aware, as teenagers do.”

Burnell comes across as having an iron will and formidable drive. “If it has taken you seven years to learn how to tie a shoelace you’re not going to give up on things easily,” she says. When she was 10 – and bored of being called by her birth name Claire – she asked people to start calling her Cerrie. At 15, she was sacked from her summer job as a chambermaid when the hotel owners ­discovered she only had one hand. “Being a seaside town, I just went into the next hotel and got a job there,” she says. In her 20s, Burnell and a friend bought a tent, went to Gatwick, and asked for a flight to somewhere sunny: they ended up camping on a beach in Gran Canaria.

She attributes her can-do attitude, in part, to her parents. “I was lucky to have parents who were encouraging and weren’t fazed by my disability,” she says.

“I feel very lucky when I speak to other disabled friends who haven’t had that kind of supportive childhood. They became more isolated in their struggle to create the kind of life they want and get the kind of support they deserve.”

Burnell says she has never yearned for things to be different. “I have never wished I had a right hand because it’s not something I could ever change. You become aware that things are harder for you, or that you have to be extra persuasive, sparkly, good at your job and charming. You have to pre-empt other people’s lack of imagination and provide them with a solution before they have even thought of it.”

As we chat, she smiles and coos at her daughter, who is playing on the floor nearby. Amelie is angelic, with huge brown eyes, honey coloured skin and gorgeous curls. She crawls at lightening speed, and Burnell’s publicist struggles to keep up. Juggling motherhood with long hours in the television studio can be difficult. “Any working mother would say it is not easy physically and emotionally, but that is the way it has to be,” says Burnell. “Sometimes my parents help out, sometimes Amelie will go to nursery.”

When I ask about Amelie’s father, a disconcerted look flits across Burnell’s face, which she quickly banishes with a smile. “I don’t talk about that,” she says. The steely look in her eye indicates the subject is firmly off-limits. But, on the subject of relationships, I’m curious as to whether her disability has affected this area of her life. “Obviously I haven’t been out with anyone who has a problem with it because, well, they wouldn’t have gone out with me in the first place,” she says.

I tell Burnell about a wheelchair-bound acquaintance of mine who gets fed up with men thinking she is a soft touch because of her disability. Burnell nods in agreement. “When you put it like that, I do get people coming up to me perhaps slightly more often than my other friends,” she says. “I don’t think they see me as a pushover, but when someone has a disability there’s more of an openness in approaching them and asking them a question. People come up and talk to me about my arm all the time.”

After our meeting, as we are leaving the hotel, Burnell asks me to switch my tape recorder back on. “Going back to what we were saying about the likelihood of posing for something like Nuts magazine, I think it would be quite revolutionary if they did have a shoot with a disabled person, but it’s not something I would ever do because I hate the way they portray women as sexual objects.” “What about for a more upmarket publication like GQ? “No,” she says firmly.

Wouldn’t she see it as a way of pushing boundaries? “It’s not a boundary I want to push, I don’t want to be seen as Katie Price,” she says. “Women are fantastic and there is so much more to them than just a pair of knockers.”

Cerrie Burnell presents Discover And Do and The Bedtime Hour daily on CBeebies.