And most galling of all, she has set up the UK's first firm offering travel insurance covering cosmetic, medical and dental operations abroad, without even knowing how underwriting worked when she started out.
Wilcox, 28, who shot to fame by winning the Channel 4 show Make Me a Million with her kids' toiletries business Halos *Horns, is in high spirits when we meet. Disarmingly confident and energetic, she has the air of someone who knows there's always somewhere else more exciting she could be.
"Why isn't there a female Richard Branson who is a women's role model?" she muses. "What everybody loves about Branson or Stelios [Haji-Ioannou, the founder of easyJet] is their personality. So many women lose their personality; they're so driven and need to be taken so seriously as businesswomen that they forget everything else. Where is their family, or do they ever go dancing?"
Dressed in white top and faded jeans, the entrepreneur talks, characteristically fast, about her second major business, Angelis, which was launched in November.
The firm, entirely funded by herself, has been set up to cash in on the ballooning market for Britons going overseas for operations from face- lifts to dental surgery.
Over 100,000 Brits travelled abroad for some form of medical treatment last year and the market is set to expand to £886m by 2010, according to a survey last year by information service Treatment Abroad.
Wilcox argues that while more and more people are looking to go abroad to save money on a range of operations, there is no cover if complications arise during surgery. Angelis's insurance acts as a normal travel policy with protection for the operation as well. It also covers any expenses for unsuccessful treatment for up to a year after the operation.
Popular destinations include, India, Eastern Europe, South Africa and Thailand, although it is only valid in accredited hospitals or clinics.
The business idea was born out of personal experience. Wilcox went to Thailand in 2006 to have breast augmentation – a treat to herself after selling Halos *Horns and paying off loans to her grandparents and mother. The operation, including a 10-day holiday in a five star hotel in Bangkok, and flights, came to £2,000 – rather than the £5,500 she was quoted on Harley Street in London.
However, her one fear was the risk of complications and the whopping bill she might then have to pay. These thoughts were compounded when months later she suffered a head-on car crash that fractured her back in three places and broke her foot.
Wilcox says her time in hospital, as well as her trip to Thailand, made her realise the opportunities available for medical tourism, and the gap in the market for an insurance firm.
Angelis's insurance for two weeks in Europe, including basic travel cover, costs £70 for dental operations and £123 for cosmetic surgery. The firm uses Lloyd's of London's largest personal lines insurer, Cassidy Davis, to underwrite the policy and has appointed the specialist travel insurer ONE Group to deal with the claims.
Meanwhile, a European Union cross-border healthcare directive is winding its way through the corridors of Brussels that would enable patients to travel to other EU countries for treatment and claim the cost back on the National Health Service.
Wilcox hopes that if this directive is passed into European Law, then the market for medical tourism travel insurance will rocket, as patients ditch NHS waiting lists for shorter waiting times overseas.
She is not concerned about her lack of experience in insurance, or the risk of competing with large providers as they join the fray. "We're the first-ever people to market," she argues. "People also trust a name, a person. I've built up the public's trust with Halos *Horns. I'm not a large corporate person and if I was going to go abroad for travel insurance, I would buy into me rather than a large corporate with no personal experience and that was just doing it for the money.
"I like brands that mean something and always have someone behind them," she says. "We put a face and a story and a reason behind our product, and I don't know an insurance company like that, with a face, except maybe the Churchill dog."
Wilcox is also open to taking on a partner to expand the online business. She says she has held conversations with a number of interested parties.
As she discusses future projects, she jumps between ideas with a Toad of Toad Hall enthusiasm, her brown eyes darting. "In 10 years' time, I want to be salsa dancing on a yacht in the Mediterranean," she only half-jokes.
"You can't fake enthusiasm. I had a fall-out with one of my business partners early on, because being an entrepreneur sounds really cool but it's not. It's about hunching over your laptop at three in the morning because you can see the end result and you want to achieve that. It's non-stop hassle – you can never switch off.
"You can't even really even call it work," she says. "It's not work, it's something you love doing – it's got to be your whole life."
There is iron determination here, yet at times a twinkle of insecurity slips through the mask of success and she seems naive to the world.
Wilcox owned a horse as a child but talks about struggling to have enough money to get by. She seems wild and impulsive – she was expelled from secondary school, and passed her driving test six days after her 17th birthday – yet she is in the hard-numbers world of insurance. Wilcox is in a rush to get off to a Fortune 100 party and her boyfriend is outside waiting in the car. She's twitching her fingers, a fist sized ruby glints.
"I wondered a few years ago how to get into hedge funds," she says, "but I want something with integrity and something I can do to sleep at night and be happy.
"I'm going to go to heaven," she concludes, and despite what's said about rich men and the eye of a needle, she's hoping Angelis might slip her through the hole.
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