No one gets all of him all the time. He whizzes round giving a commanding performance, quite unlike anyone else. He is a one-man company doctor, a fixer nonpareil, with an astonishing reputation, among politicians and the City and business, for getting things done. He does not have clients in the true sense: he is not a partner in a large service agency. If any label describes him, it's management consultant, but one valued so highly that organisations invariably ask him to join the board.
Stevenson's list of past and present directorships and chairmanships runs and runs. At present he chairs Pearson and GPA; he is a non-executive director at BSkyB, The Economist, Manpower and Lazards; he advises Tony Blair on implementing new technology in schools, and is trying to knock heads together for the Prime Minister on funding the arts; he advises the Law Society on how best to reform itself; and chairs the trustees of the Tate Gallery and the Sinfonia 21 orchestra. Until recently he was chairman of the Tate's trustees, and his strategic consultancy, SRU, that he founded with Peter Wallis, has advised companies such as Unilever, BAT and EMI.
At 53, he is a millionaire several times over, moving easily between corporate power-broking and social policy think-ins. He advises New Labour, but once worked for ex-Tory minister Peter Walker. Both parties have unsuccessfully wooed him to run for safe seats. Remaining avowedly apolitical, he's become a bridge between New Labour and business - introducing Blair to key corporate figures.
"He is not like other businessmen we are close to, who are known to be Labour," says a member of the Blair inner circle. "Stevenson scores by not being anything. He is close to the Prime Minister. He's used, and uses himself, in a selective, discreet and serious way. There is always that knowledge with Dennis that the Government needs him more than he needs the Government."
In private, Stevenson is classically New Labour, talking a strong centre- left argument but remaining avowedly pragmatic - and commercial. Stevenson is passionate in his belief that people, especially those like him, should pay their taxes "to create a stable society".
To meet him is to be swept along on a mixture of familiarity and charm, self-deprecating one minute, unapologetically self-promotional the next. He is courteous without being pompous, authoritarian without being ridiculous. He doesn't power dress, eschewing establishment pinstripes for more fashionable labels, and he is as much at home talking about his four sons and their passion for football as he is discussing Pearson's future. It is this sense of being apart that's distinguished his career and has been the bedrock of his success. He has never been anything but an independent operator. He comes without baggage - a self-starter who taught himself, who relies on instinct when others reach for textbooks.
He is the son of a Scottish farmer and an English mother who, after her husband died, returned to teaching history of art at university. Stevenson, setting the pattern for his later balancing act, read both classics and economics at Cambridge, before going into management consultancy. Within three years he had his own firm, with Wallis. From the outset, he showed a lofty disdain for the normal. While other firms rushed after potential clients, he researched rates of employment of black people. He was 24 when he rang the Financial Times, a paper that he would one day technically control as chairman of its parent, Pearson, and suggested it publish his study. The FT gave it a generous half page.
News of Stevenson's report soon reached Peter Walker, then in Edward Heath's government and a minister always keen to seek advice from outside the stuffy confines of Whitehall. The patrician Walker and the earnest but confident graduate took to each other. Walker asked him to look into youth affairs, which resulted in a report that was critical of the government's plan to curb pop festivals. A newspaper dubbed him Mr Pop.
Walker asked Stevenson, then 26, to head the Newton Aycliffe and Peterlee New Town Development Corporation. In what was one of the first big Japanese inward investment deals, he helped persuade NSK, the rolling-bearing maker, to set up in Peterlee, in the North-east, creating thousands of jobs. He remained in charge from 1971 until 1989, after the arrival of Mrs Thatcher with whom the fledgling fixer and smoother of differences could not see eye-to-eye. Stevenson then moved away from what he calls "public service" and developed a formidable corporate advisory practice. His stature increased with that of the people he worked with, such as Niall FitzGerald of Unilever and Sir Colin Southgate of EMI.
Two events brought him out of the shadows of the City and Westminster. First, as a non-executive director of Manpower, he sparked the Blue Arrow affair by drawing the attention of fellow directors to the extravagances of Tony Berry. The City, sensitive to accusations of corporate excess, turned on Berry and embraced Stevenson.
His reputation was made as an honest broker, a firm negotiator who wouldn't be swayed, later reinforced by the skilful way he steered GPA through debt rescheduling.
This stood him in good stead as firms grew increasingly twitchy about being seen to behave properly - a reputation he nurtures, making the point that he is dependent on no one and won't be bought.
The second event flew in the face of Margaret Thatcher, who'd seen him as too far to the left. The trustees of the Tate exercised their right to have an outsider as chairman and turned to Stevenson. With Nicholas Serota running the gallery and Stevenson controlling funding, the Tate was transformed - and it assured Stevenson's entree to the upper reaches of arts administration, where politics can collide with corporate sponsorship.
Stevenson's style was also suited to Pearson, where he has developed a rapport with Marjorie Scardino, its far-from-conventional chief executive. And Pearson gives him a foothold in finance, as it holds shares in Lazards, the merchant bank, and a foothold in media - there are few better bridges between business and politics than chairing the group that owns the FT.
Pearson also provides Stevenson with links to publishing (Penguin books and Simon & Schuster), leisure (theme parks) and broadcasting (TV holdings).
In a company crying out for a fresh approach, Stevenson and Scardino have delighted in cutting through bureaucracy and traditional - but often nonsensical - ways of doing things.
This article is taken from April's `Management Today', published 31 March, at pounds 3.50. Subscriptions: 0181-841 3970