“I’m 8ft 4in trapped in a smaller body,” laughs Kevin Beeston, patting his sizeable tum. Young, jowly, blue-eyed, the demotically charming Beeston clearly enjoys being something of a surprise.

For he is not, by any stretch of the imagination, what you would expect to find as the executive chairman of a £767m group that runs top-secret projects such as the Atomic Weapons Establishment at Aldermaston. But then Serco, the support-services group that takes public services private and has expanded exponentially from its defence-contract roots, is not much like other plcs anyway.

For a start, few would bundle together railways, prisons, hospitals, leisure centres and the odd bit of nuclear-missile work, but Serco does. And under Beeston’s watch, it appears now to be sloughing off its previously media-cautious approach. Last year it even had the first picture of its senior executive team in its annual report (buried at the back, surrounded by schoolkids in a Wallsall playground where Serco runs education services). Goodness me.

Beeston shrugs in a good-natured way. “The reason we have adopted a low profile,” he explains, “is not because we’re secretive, it’s probably just because our customers have never wanted us to be highly visible.” Those customers being, of course, various government departments that provide more than four-fifths of Serco’s work. That now stretches from sensitive defence contracts — Serco emerged from the remnants of the electronics firm RCA’s UK service operation, which ran Britain’s ballistic missile early-warning system — to transport, leisure, education, prisons, healthcare and more.

And, leaving Beeston’s tubbiness to one side — he makes quite enough jokes about it himself — it has been some growth curve. The willingness of the last three British governments to shift more public services into private hands means that Serco has expanded its turnover at a phenomenal rate, averaging 20% a year since its flotation in 1988. It has also managed to avoid a lot of the flak that has flown at its better known rival Capita, despite its concentration on more front-end work.

How? Serco would argue that it is because it manages contracts efficiently — its Docklands Light Railway (DLR) has won rail company of the year twice — and humanely, running a people-centric business and drawing on a corporate culture that goes back to when RCA first set up in Britain in 1929.

Top executives have to work their way up, teams come before individuals, background counts for nothing. The affable Beeston, just 41, the son of an Ipswich mechanic, joined the company at 23, having jumped ship from Unilever because it would not fast-track non- graduates. Look at him now.

Others might say that Serco has just been smart keeping its head down. It is highly respected where it matters, by the government, and has used those long-term defence links to snaffle up an ever-longer list of contracts.

The firm is, literally, everywhere: running National Rail Enquiries, managing Royal Navy ports, operating the National Physical Laboratory (Greenwich Mean Time), building the new Joint Services Command and Staff College, sorting out Merseyrail light railway, providing IT for the National Crime Squad, selling non- clinical services to Norfolk and Norwich University Hospital private-finance initiative, opening Dovegate Prison — and that’s just a clutch from some 600 contracts in total. All are fixed-term, and the beauty of it is, according to Beeston, the income is assured.

So no 4am worries about its markets collapsing and the company plunging into the red? It couldn’t happen, says Beeston. “None of the contracts forms more than 5% of group turnover, all are self-contained. If we lose one, we lose 5% of the cost base, too. And there’s nothing that could make us lose all the contracts at once.”

If that sounds too rosy, they don’t win them all. Serco bid for the National Air Traffic Services public-private partnership, and lost. It bid to run London’s congestion charge, but was undercut by Capita. As Capita is now having difficulty making the system pay, you would expect Beeston to be chortling, but he remains impassive. Any slip-ups by other support -service firms reflect badly on them all, he points out.

And there are some sizeable banana skins to avoid. Not everyone is comfortable with the increasing all-pervasiveness of firms like Serco, nor the fact that the same people who provide non-clinical services to hospitals should also, for instance, be the biggest organiser of electronic tagging for offenders and profit from prisons.

Sitting in the firm’s beautiful Regency-repro offices overlooking the Thames in Richmond, southwest London, Beeston begs to disagree. He points to the studies of private-sector prisons that show standards are higher, staff better motivated, and prisoners better treated. He is, as you would expect, a bouncy proselytiser for the Serco cause but he never veers from the logical and provable.