He is sensitive about his figure, claiming recently to be a stone more than he should be but a stone under his maximum weight. He looks big, talks big and thinks big.
He comes across in public, at least, as everybody's favourite uncle. Softly spoken with a large, round face and a jolly smile, he has the ability to put people at their ease. In private, though, colleagues testify to an occasionally more serious and testier side. A smaller man would shout and throw his arms about; Davis need only stare.
It is a withering look that throws his opponents off-balance. Far more effective than histrionics, it means people stand aside.
Similarly, criticism of, say, his salary (which rose by a quarter last year to pounds 390,000), or his unfashionably dual role as chairman and chief executive, or the price he paid for Octopus Books, are firmly dismissed.
Over lunch not long ago in the palatial Reed headquarters in London's West End, he tended to talk and the other diners listened. The conversation wandered over a range of subjects dear to Davis's heart - industry gossip; why some publications sell and others don't; and - as this was part informal meal, part biographical interview - his early years and his climb to the top of Reed.
He was born the day before Christmas Eve, 1941, the son of a Merseyside cotton trader. Like many others who travel south to seek their fortune, he still regards himself as a Northerner. But attendance at a well-known public school, Shrewsbury, and a rounded, well-bred accent betray a background far removed from Coronation Street and frothy beer.
At school he was not an outstanding sportsman or academic genius. What he was, though, was a good talker, being a keen actor and member of the Young Conservatives (his friends say he would have made a natural politician).
It was appropriate, therefore, that after leaving school with two A-levels and spending a short period as a storeman, he should find his feet as a travelling salesman with a small engineering company. For five years he toured the country, haggling, pushing, selling.
In 1965, he switched from selling to a more cerebral role in marketing for General Foods, 'for half the salary and no company car'.
There was method in his madness, though. General Foods was simply the next stage in a carefully mapped route. At 22, he had told his boss he wanted to run a big company before he was 50. He made it at 44.
He knew how to sell, now he learned about branding, product development and corporate politics. He was in good company. A fellow product manager at the time was James Blyth, chief executive of Boots and now one of his closest friends; Blyth is godfather to his daughter, and Davis sits on the Boots board.
Nine years later, he joined Fitch Lovell as marketing manager. When it was time to move on again, after just two years, he did not bother with scanning the Jobs Vacant columns. He wrote to David Sainsbury on the off-chance, asking for a job. Sainsbury said yes, and within a year of joining, in 1977, he was marketing director.
Most would have settled for J Sainsbury. He rose to assistant managing director, deputy chairman of Homebase and one of the troika that ran the company. But he wanted his own show.
In 1986, his ambition pushed him on again and he contacted a headhunter. There was just one stipulation: he was contractually bound not to work for a competitor. By chance, the headhunter was searching for a new chief executive for Reed, then a disparate collection of businesses ranging from paper mills, shower fittings, wallpaper and gas boilers to such magazines as Horse & Hound and Country Life.
Profits of only pounds 100m from annual sales of pounds 2bn had marked the company down for corporate dinosaur status. Before taking up the reins, Davis spent six months touring Reed's operations. By the time he started, in November 1986, he knew what to do: Reed's future lay in publishing. The rest, worth around pounds 1.5bn, would be sold.
He stuck to his guns, disposing of everything bar the publishing division. At the same time, four big acquisitions catapulted Reed into position as Europe's third biggest publisher, behind Bertelsmann, the German group, and Hachette of France. Davis had bought Octopus Books for pounds 533m, TV Times for pounds 123m, the Travel Information Group, a United States travel guide producer, for pounds 535m, and, finally, Martindale-Hubbell, the US legal publisher, for pounds 189m.
While some of the prices paid - especially for Octopus - seem high, profits, on reduced turnover, have more than doubled, to pounds 240m.
Strangely after such a radical shake-up, the man who was doing the shaking likes to pride himself on being cautious and methodical. For instance, he claims that he loathes making sealed bids - for fear of paying too much.
If he has a significant failing, it may be that caution can take too long. Reed may be merging with Elsevier, and it has transformed its appearance externally, but company insiders claim that it is only now, some six years on, that Davis has got around to really addressing some of the internal problems.
He takes his position seriously. He sits on the ruling bodies of no less than seven non-Reed organisations, including the NSPCC, Business in the Community and the Adult Literacy and Basic Skills Unit.
Yet that very seriousness can make him appear vain. Before accepting an invitation to the annual City publishing analysts' dinner he once apparently rang round other company chiefs to check that guests of similar stature would be there.
One journalist who crossed him was removed from the company's invitation list and only restored after pressure from his boss.
Davis's caution extends to his family. Married with three children, he will not give their names because he doesn't want them to suffer discomfort for having a 'successful father'. Neither will he take his chauffeur-driven Bentley to his daughter's school, since there is no way of telling how people may react. His two sons were sent on a Pru Leith cookery course and encouraged to learn to operate word processors, to make them more useful individuals.
When he is not running Reed, he can usually be found at the weekend sailing his yacht - at the helm, of course.
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