As a television presenter, Holland lacks any of the usual qualifications: fluency, bouncy confidence, or a love-me-please demeanour. And though he is an almost automatic first choice to present contemporary music shows, his own music is rooted in the past, in blues and boogie-woogie. But perhaps it is these paradoxes that are the key to his persistent edgy fashionableness (not least at the moment when Channel 4 is showing The Best of The Tube, the BBC is repeating Later, Toothbrush has just finished its run, and the Jools Holland Big Band is about to go on tour).
Holland is 37 now, but his office is a boy's bedroom of a place, its heterogeneous clutter revealing his obsessions: motorbike helmets, old records, videos, books on Hogarth and Pepys, architectural drawing, Dinky toys and a telescope. His clothes similarly project a style that is too wackily pick 'n' mix to be pinned down. He loves uniforms, and when he was younger and obsessed with motorbikes was "always covered with oil and stuff. It was kind of a fashion thing at the time to dip your hair in the sump of a lorry." He has recently bought a model steam lorry, one- sixth the size of an original, and is "trying to think of myself as a steam man. I think overalls more than leathers, maybe a leather cap. Anyway, it's nice to get dressed up, whatever the event." Today he is wearing a roll-neck fisherman's jersey, jeans, sports jacket and pointy boots, the uniform of the off-duty musician.
He seems to treat the world as a theme park for his own amusement: his studio and office occupy what appears to be a disused railway station. Helicon Mountain, which he describes as "the jewel in Greenwich's architectural crown", comes complete with a sign saying "Ladies and Waiting Rooms", a white picket fence, a cast-iron twopenny chocolate machine, and an advertisement for the Sunday Pictorial.
An elderly passer-by once told him it was lovely to see the station so beautifully restored - she remembered being taken there as a child to start her holiday. But though the scruffy services of Network South East trundle through the cutting below, trains have never passed through romantic Helicon Mountain, which is an idealised Legoland station created from a jumble of stables and lock-up garages - a modern folly.
The same spirit of playfulness sends his conversation spurting off in unpredictable directions. After answering a few questions about his ubiquity, he says: "But at the end of the day, they're all just television programmes. My advice to people would be not to watch television at all, and talk to their families."
Quite a few people, I suggest, might find this rather gruesome. "Well actually, thinking about it, yes. Not their own families, I hasten to add. Other people's."
He is constantly slithering away into facetiousness like this. For much of his childhood, the family didn't have a bath, "but that was good, because I didn't like baths. And we didn't have any electricity, but that was good because it gave me an opportunity to learn how to operate paraffin lamps".
So what did his parents do? "Well, they didn't get me a piano. My mother had twins when I was eight, which prevented her from doing anything, and my father would take me round museums."
But did they work? "My father had various excitements as far as work was concerned, and ended up - I'm not quite sure how it happened - going from being skint to being quite comfortable at one point. Suddenly cars and televisions and larger houses appeared. I decided to move out at that point."
Holland surrounds himself with people who operate at a similar level of unseriousness; he's much more interested in putting an amusing spin on the conversation than in excavating his feelings. Vic Reeves and Bob Mortimer occupied one of the Helicon Mountain offices until recently; another comedian, Norman Lovett (once of Red Dwarf), is living in the Edwardian showman's caravan parked outside the station. We talk about his time with Squeeze. "Obviously we had no morals about drugs or sex or anything." And I wonder how long this went on. "Till about 1994," he says.
His father seems to have taken a similar, but, for his family, rather less benignly insouciant approach to life. Derek Holland's erratic way with work (he was never in the same job for long) was matched by a similar approach to family life: he and Jools's mother split up when Jools was 11, got back together and split up again. "He wasn't really suited to marriage," his son says now. In 1988, Derek Holland served 15 months in prison for stealing £35,000 worth of jewellery belonging to Jools's girlfriend, Christabel. I remark that his father sounds a bit of a handful, but typically, his son doesn't want to talk about the jewellery incident. "Yes, he is. He's a laugh sometimes."
Derek moved the family around London, avoiding rent collectors, until they settled in South-east London, where Jools's grandmother lived. She had a pianola in her front room, on which, when Jools was eight, his uncle taught him to play the St Louis Blues.
That was the limit of his repertoire, but Jools was hooked: he bought blues, jazz and boogie woogie records and taught himself by ear. Apart from "completely un-fun" theory lessons at school, he had no formal training, "but I didn't mind because I wanted the sound that came out to be mine". Boogie woogie is about rhythm and individuality, rather than the finer points of technique; personality is what matters most. "If you're a painter," he explains, "being able to copy a picture by Poussin precisely isn't going to help you much - unless you're never really going to be up to it. I do that with architectural drawings: I copy other people's and they look like complete shit, but it's very improving."
At 16, Holland was asked to leave Shooters Hill grammar school after a series of smoking and hiding-in-the-wood incidents culminated in the bouncing of a teacher's car across the playground to retrieve a sixpence that had rolled underneath. "And as I am sure children are still told today, we could easily have been killed doing that, and it was possibly a matter for the police."
But by then he didn't care, because he was playing in pubs with the guitarist Glen Tilbrook, earning a bit of cash, "and we were much more cocky and confident than we had any right to be, and thought we'd be a huge success."
As Squeeze, which is what they became with the addition of two more members, they had two singles reach number two in the British charts and considerable success as a touring band in America. Gilson Lavis, Squeeze's drummer, now supplies a key ingredient to the Jools Holland Big Band sound, "giving it kick and aggression, making it thrusty, not like a rather dreadful showband or something. And then the horns come out of jazz but the rhythm section's like a rhythm-and-blues rhythm section, so it has this sort of meshing thing".
The viewers' sense of Holland's musical integrity is crucial to his effectiveness as a presenter. On The Tube his preference for old black men and their music relieved Paula Yates's excitability about young white men and their bodies. He claims his role on Toothbrush was simply that of musical director; but as he acknowledges, the music "could easily have gone down the twee route", and it didn't. About Later he is even more modest - "you could do it with a few captions, but of course a lot of people can't read and write, so I suppose I help from that point of view". But the truth is that musicians want to appear on Later not because they are vastly paid or reach huge audiences, but because it's cool. It wouldn't be at all cool with captions.
At the age of 24, Holland moved in with his girlfriend Mary, a hairdresser, and they had two children, George and Rosie. But then in 1987, on location with The Tube, he fell in love with the 23-year-old mistress of Bamburgh Castle in Northumberland, Christabel, Lady Durham. They have lived together ever since, a boy with such deadened south London vowels that his voice sounds almost inherently funny, and a woman whose son will inherit an earldom. Christabel is a sculptor, "though currently Mrs DIY, or Mrs DIY Overseer", because they, her son Fred and their daughter Mabel, recently moved into "a bigger leafy suburban semi". George and Rosie visit most weekends.
Though not exactly defensive about his family (beyond saying that he does the lottery in the hope that it will alienate them), Holland isn't expansive either; and on the whole it's more rewarding to talk to him about his model railway and Minic motorway, though sadly these have been broken up since the family moved. The layout included a model Helicon Mountain, a red light district and a crack house, and during general elections they would put up Kinnock and Major posters.
Jools Holland is a very British celebrity. There is something about him reminiscent of Terry-Thomas, and it isn't just that he sometimes wears loud, chalk-stripe suits. He is an eccentric, his boyish enthusiasms never taken too seriously, stylish but beyond fashion, theme park man but with a saving seriousness about music. But Holland himself - who returned to The Tube after a six-week suspension for swearing to announce that he'd spent the time "travelling into Bob Monkhouse's subconscious" - would think this was ridiculously pompous. Anyway, it's time to look over the caravan and consider curtain possibilities.