But he and his double-act partner of 20 years, Mel Smith, have never been the last word in trendiness - which may be one reason why they've lasted so long. "We've never been enormously fashionable," he confirms. "We're not new or cutting-edge."
This has not, of course, always endeared them to dedicated followers of fashion in the press. "If we do stuff based on a routine music-hall relationship, we tend to find ourselves having a rough time with the critics," Rhys Jones says, more in sorrow than in anger.
By the same token, even at the peak of the satirical BBC sketch-show which made his name, Not the Nine O'Clock News, Rhys Jones did not see himself as a barricade-stormer in the fabled alternative comedy revolution. "I never liked the term 'alternative comedy'. It came along after that ethos had already bitten the dust. It's quite a shock to be called 'former alternative comedians', because true alternative comedians had no idea we were included in their number. We came across as middle-class and not too much out on a surreal limb. Time Out was the first to decide that Not the Nine O'Clock News was a bunch of middle-class wankers wanking. By that measure, we could never call ourselves alternative. We just haven't worn enough black Dr Martens."
Greying at the temples now, the 44-year-old Rhys Jones is perfectly happy to leave niche "yoof" programming to those closer in age to the target market. "A couple of years ago, we decided we didn't want to chase the youth vote. It's that Tony Parsons cult - 'I'm the voice of young people, even though I'm getting on for 50'. The cult of youth, the assumption that youth knows all the secrets of life, is a load of tosh. People like Janet Street-Porter, Lee and Herring and Ben Elton all refer to this mythical 17-year-old who's honest and knows what's what, while the rest of us are just sad, middle-aged characters who have lost our way. I love being middle-aged. I don't like 17-year-olds.
"When I was 18, I was perfectly happy to watch the ordinary news. I didn't need the news presented by young people in trendy clothes. Good television like Blackadder or Vic and Bob attracts a broad audience; the idea that it has to be youth-orientated is redundant."
For all that, Rhys Jones doesn't seem quite ready for the pipe and slippers yet. A nervy bundle of energy unable to sit still for long, he makes for invigorating company. When he laughs - which he does frequently - his face creases up so much, his eyes disappear. Ideas bubble out of him like fizz from a shaken Coke can.
When we meet at a location in Berkshire for the new series of Smith and Jones, he is enthusing about the morning they have just had, shooting sketches involving a clown car. "Sometimes our stuff is witty, and sometimes it's at the level of a clown car. I don't like topical comedy. I find it only serves the politicians' idea of their own importance. Nothing flatters the whole political ethos more than making sketches about it. We'd get lots of ticks if we did sketches about Peter Mandelson, but we'd prefer to make jokes about clown cars."
Smith and Jones have endured, he reckons, because of the endless possibilities thrown up by a double act. "Double acts work on television because television prefers drama to in-your-face talking heads. Viewers get tired of stand- ups. Les Dawson and Ken Dodd both had success on television, but they got less bedded-in because they tried to do their stage act on television, and they're two different mediums."
The partnership between Smith and Jones also stays fresh because they don't spend all their time in each other's pockets. Smith is a director - he helmed last year's box-office smash, Bean - while Rhys Jones has his finger in many pies. In addition to the TV series, he is working on two radio programmes - Do Go On, a spoof Start the Week-type show, and The Mitchells, a comedy about a family afflicted by all the disasters you read about in the tabloids.
Rhys Jones has also just completed an acclaimed run in The Front Page at the Donmar Warehouse, but he is disarmingly modest about his stage acting. "I only have one performance," he laughs. "The first time I did it, I got the best reviews anyone has ever had. Now it's the law of diminishing returns. Sometimes I put that performance to work on an inappropriate subject, and I come a cropper. A season at the RSC would terrify me to death. Within that would be the seeds of failure."
Oh yes, and with Smith he runs an independent production company, Talkback, which makes such shows as They Think It's All Over and Never Mind the Buzzcocks. In the midst of all this activity, Rhys Jones managed to fit in recordings of Crystal Balls, an occasional series which "shows how futile prophesies are". In it, he reveals, for instance, that "the director- general of the Zambian academy of space research predicted that the first Zambian astronaut would reach the moon by 1965 using a very large catapult."
If there is one area where Rhys Jones remains unfulfilled, it is in films. Admitting that his foray into the cinema with Morons from Outer Space was "not a huge success", he laments the lack of suitable screenplays. "Peter Sellers wanted to do comedy films, but he couldn't get the scripts. No matter how funny you are, if you don't have the script, then the film's a lulu. You can't come on and read the phone directory and hope to be funny."
For the moment, however, he is quite happy with the way things are. "We're still knocking around. It's frightening to think how long we've been doing it now. We keep expecting someone at the BBC to say 'That's enough of all that', but they never have. If we go on long enough, we'll reach cult status. As Alan Bennett said, you just have to get over the age of 60 to become a national treasure in this country. I assume we'll just toddle along on a wave of indifference till then."
'Crystal Balls' is on tomorrow, 10.10pm, BBC1. 'Smith and Jones' begins a new series in the autumn