Or perhaps they would do so even more regularly to wind him up.

As it is, Cullum’s boyish demeanour rather matches his diminutive stature. Although his new single I’m All Over It is possibly his most radio-friendly yet, and he fills concert halls and headlines at festivals, he still loves to join the jam session in a local club afterwards. Finger on the pulse, he was one of those at hip American band of the moment Grizzly Bear in London last weekend. “Stunning,” is his verdict.

Launching his new album The Pursuit (out on Monday) in Manchester’s equally cool and tiny Matt and Phred’s Jazz Club, Cullum bounds on stage, full of self-deprecating stories, and is on his feet and off the piano stool as much as he sits on it. He is rather too full of boyish enthusiasms to be much concerned with paparazzi shots of him and his intended that are clearly designed to accentuate the 15cm height difference between them. He should worry. I once had the pleasure of meeting Ms Dahl, when she was dating Scots actor Douglas Henshall, and I can confirm what the envious lensmen probably think: the lad has done rather well.

It would be going much too far to suggest that Dahl is all over the new disc, but there is no doubting her presence. What is the pursuit to which the title refers, one might wonder? Who was the recipient of the lovingly compiled Mixtape, celebrated in the song of that name? There are a couple of direct and sincere love songs – Love Ain’t Gonna Let You Down, and I Think, I Love – which are much too honestly expressed to be anything other than dedications to the lady. Cullum doesn’t deny this, but equally he is unwilling to have his new album summarised as an account of their affair.

“I’m not a diary songwriter, so there’s nothing that relates too directly to my life. I’m a semi grown-up human being,” he insists.

Somewhat incredibly, it is five years since the last Cullum album, Catching Tales, which had a rather less acoustically suitable showcase launch in Glasgow’s Princes Square. The difference is quite remarkable. A female colleague has noted that the stylish Dahl may well have had an influence on Cullum’s much-improved dress sense, but the change is more fundamental than that.

Since he last promoted a disc, Cullum has stepped back a little from the jazz world he sprung from. He made some electronic dance music with his older brother and turned up at places to DJ, with a box of vinyl from his extensive collection. Thanks to an introduction from Clint Eastwood’s jazz bass-playing son Kyle, Cullum also worked in the soundtrack to the movie Gran Torino, picking up a Golden Globe nomination for his song.

He’s genuinely excited about this development in his career, which followed a contribution to the soundtrack of John Cusack’s film Grace Is Gone. Cullum’s university education was in English and Film at Reading, not music at all, and he is delighted to be making some beleated use of that.

All of this breadth of interest shows in Cullum’s writing. Alongside clever arrangements of Cole

Porter’s Just One Of Those Things, Leslie Bricusse’s If I Ruled The World and Rihanna’s Please Don’t Stop The Music, the nine originals on The Pursuit are, indeed, the work of a mature songwriter and a few of then would look comfortable in the repertoire of more mature voices than his.

“In the last couple of years I’ve written a lot of songs. I had far too many for the album – about 30, ” he said, explaining that he and producer Greg Wells made their choices from the work that Cullum had done in his own Terrified Studios in London’s Shepherd’s Bush.

“The selection was up to me, but I’m always willing to take suggestions. These are not necessarily the best songs, just the ones that worked best on the album. It is a terribly old-fashioned way to make a record these days, but this is unashamedly an album to be listened to all the way through.”

That boyishness is indeed tempered with a sense that Cullum is an old-fashioned gent. Although Mixtape is one of the tracks that successfully employs what he has learned from dabbling in electronica, its subject matter – compilation cassettes – is hardly cutting edge technology. Terrified Studios are so named because of his admitted techno-fear. And then there’s the vinyl.

“I’m a record geek. I collect vinyl. I’ll buy the heaviest vinyl they’ve got.”

Although the final recording was made in Los Angeles (still employing the talents of Cullum’s regular live band: drummer Brad Webb, bassist Chris Hill, saxophonist and keyboard player Tom Richards and guitarist and trumpeter Rory Simmons), some elements of Cullum’s home recordings survive in the final mix. For him that’s indicative of the ease with which “anyone can record an album now”.

“It is a gift to be a musician, but it is hard to make it your job. If you succeed, that’s a privilege not to be taken lightly.”

Cullum is very precise and hands-on about this. He knows exactly how well his records sell in each territory across the globe and divides his time accordingly. It might seem many months between the release of the album at home and his UK concert dates, but there are commitments in Japan, Australia and the US to fit in before then. Any wedding to Dahl is clearly not happening until after all of those commitments – and it is unlikely that the paparazzi will receive an invitation.

“I’m not a natural self-publicist. My background is in playing music, not being a personality.”

The Pursuit is out on Monday on Decca. Jamie Cullum plays Glasgow Royal Concert Hall on May 7 and Edinburgh’s Usher Hall on May 8, 2010.