So serendipitous is the story of how Saima Khan ended up running her upmarket catering business, The Hampstead Kitchen, that you couldn't actually invent it. And when we meet at her Hampstead flat, in which she has promised to cook me lunch, Khan is fussing over the presentation of the beautiful dishes in front of us while telling me about the day that she bumped into Warren Buffett in an airport lounge in Omaha.

"So he asks me this question: 'when was the last time you were excited?' and I couldn't answer him," she says, laughing.

Eventually Khan, then 20 years into a City career and working in credit and market risk strategy projects for Buffett's company Berkshire Hathaway, told the billionaire magnate of an occasion where she had filled in at the last minute for a top chef who had failed to turn up to a small private cooking job.

Having hosted dinners for friends since her university days, Khan was a keen cook but had no catering experience. "I was there in my apron, blagging it, thinking someone was going to find me out, then at the end they all said 'bravo', thanked me and I just thought 'this is amazing'. One lady even asked if I'd cook for her at her house in France. That was a Saturday in London, and then I had to go back to work in New York two days later."

Buffett, surprised that Khan had taken so long to answer him, suggested she revisit that memory. "He said: 'You're not living at the moment. You're surviving. If you can't tell me what inspires you, and what your passion is, then what are you living for?'"

A month later, Khan ended up cooking curry for Buffett and his wife Astrid at her flat in New York.

Bill Gates adored Khan's food and told her he wanted to start a business

The month after that he returned with his friend, multi-billionaire Bill Gates, in tow and it turned out that not only did Gates also adore her food, but that he and his wife had also done some work in the Pakistani village that Khan's parents had grown up in. More importantly, he wanted Khan to start her own food business.

"I was like, 'What sort of joke is this?' I became tongue-tied and really nervous. He said to me: 'Oh, go on. You have such a talent, you know how to engage people with the food, and you can do it!'"

It wasn't until a family friend passed away and she soon bumped into Buffett, who asked about her business plan, that Khan stuffed her suits and smart handbags into a wardrobe and The Hampstead Kitchen was born.

Today, Khan is a full-time caterer who runs between two and eight events a night, the majority of which are in London, with others anywhere from Barcelona to Qatar. These could be a dinner for ten people in their home – "I get so much business from word of mouth in Hampstead." – to a banquet of 500. Regular clients are mostly unprintable, being a selection of A-list actors and actresses, presidents, or international royal families; she also recently catered for the Climate Change Summit in Paris.

Born to Pakistani parents in London, Khan says she inherited little food knowledge from them – other than her mother's "speed of cooking" and her father's love of simple presentation.

Inspired by years of eating around the world, she won't be pigeonholed by her food, saying she can make anything as long as it's "a cuisine based around a sharing concept", and indeed her Instagram feed throws up all sorts – a platter of baby spinach, rocket and orange and orange blossom salad, a plate of smoky aubergine, smoked paprika and mascarpone blinis, or pomegranate, strawberry and rose Eton mess.

"People hire us for our colourful and well-presented food. I call it 'food without borders' – just because you belong and may have ties to a country, it doesn't mean you only have to represent that country," she says.

At this point Khan howls with laughter as steam whooshes up from a pan of sea bass. But she insists I dive in to try what she has prepared. There is a glorious onion and garlicky yoghurt side dish that Khan now calls 'The Magic Dip' after it became a firm favourite with a well-known president's wife, there is a smoky paprika hummus, roasted red peppers with walnuts, the most delicate and nutty falafel, and then the pretty sea bass alongside salads of wild rice and baby courgette, and fennel, orange, and rocket. There are bright, intense flavours to each dish, and I can absolutely see why her regulars stick by her.

Saima Khan at her home in Hampstead

But how does she manage it all? Khan says she only hires people – she currently has 170 freelance staff from waiters, to prep cooks and bar help – whom she trusts and whom she has picked out herself. She also has two kitchens where all the prep work is done.

"I match staff according to my client, the event and the setting. For example I have an amazing team that also works during the day for corporate hospitality for Coutts, and are great for formal embassy and heads of state dinners. For a family dinner, we have extra-friendly staff who ensure the host is at ease."

She claims she can appear at three events in one night – "because I can pop in for dessert, or before the dinner, and tell them all about what we do" – but relies on her staff to send her pictures before each event so she can keep tabs on how it's all going. "I'm really anal, so yes, I'm quite involved," she laughs.

But despite the focus on presentation, and the fact two of the most famous businessmen in the world continue to mentor her, there is no pomp to what she does; Khan's favourite events are "the ones at home, where they don't show off and it's just about pleasing their families and friends."

Finally, I ask if she misses her old life: "I don't miss the time that it takes out of your life – that sucks everything out of you… My life has become so much happier. But when all that ["travelling on first class, working at one of the best companies in the world, having a personal trainer, amazing shoes and handbags"] goes, you're just left with yourself, and you think 'what am I made of?'"I'd say she's made of pretty strong stuff.