IT’S the phone call many executives dream of: Richard Branson saying, hi, come on over for the weekend, we’ll talk about setting up a new company, you’ll head it and we’ll float it for a billion five years down the line.

“It was,” giggles Tom Alexander, chief executive of Virgin Mobile, “a bit like sleeping with a very sexy woman.” He couldn’t resist.

So he chucked in the day job at BT Cellnet and this weekend here he is, contemplating the prospect of heading the biggest flotation brought to the British stock market this year.

And is he worried? Er, not quite. More likely he can’t believe his luck. Tanned and charming, with thinning hair cut long, stripey shirt tucked into dark chinos, Alexander, 44, looks as if he’s struggling to suppress the biggest of smiles.

After a varied career that has included professional go-kart racing and telecoms sales in Scandinavia and America, this mildly dyslexic, former public schoolboy (sound familiar?) is about to make serious money.

Few would deny him his reward. What Alexander has achieved in five years with Virgin Mobile is an extraordinary triumph in branding. Using network time rented from others, he has attracted over 4m UK users to a service that offers little more than sharp pricing, clever positioning and efficient customer service, especially popular with those who want something cheap and simple.

Where’s the technology? He doesn’t need it. “We’re not an engineering company,” he says, “we’re a marketing and service company. That’s the model.”

As a “virtual operator” — Virgin Mobile buys its airtime from its former partner, T-Mobile — he doesn’t have to pour money into capital expenditure. Other networks maintain the base stations, while his offer is about “attracting customers, keeping customers, passionate customer service” and the power of the Virgin name.

“I know you’re sceptical,” he says, rather engagingly, “but the Virgin name is an incredibly powerful brand. If you go into a supermarket and watch people looking at all the models of phones on offer, which is the one that the customer picks up? It’s the Virgin Mobile box. The name gives us a head start.”

As he sits in his cramped corner office overlooking London’s Leicester Square, Scalextric set in one corner, whiteboard decorated with doodles by his seven-year-old daughter propped behind, Alexander exudes low-key enthusiasm.

Those who know him remark on his unassuming style and his determination to grow the 1,400-employee business with a flat, non-hierarchical structure. So far it has worked, allowing him to create the biggest virtual-network operator in the country, outstripping rival operations launched by Tesco and Carphone Warehouse.

“The thing I love about this business is that we’re having a ball,” he says. “It’s like leading a winning football team, win after win after win — you run on adrenaline.”

So why divert everyone by floating?