Chris Maume: You don't have to be old and grey to listen to Radio 1, but it helps...

Greetings, pop pickers! Have we got a show for you today! Pipe smoking: is it the new meow-meow? Followed by Men's Hair Dye of the Week! Then we've got – cue drum roll and jazzy jingle – Lady Gaga coming in to talk about her all-time favourite chunky-knit cardigans! All yours on super, sedentary Radio 1! First up, here's Dame Vera Lynn and her cover of "I Want Your Sex"!

The nation's favourite pop station has a problem, it's been alleged: its audience is greying round the temples. These are the figures, according to the GMG Radio: although its target age is supposed to be 15-29, nearly 2.5 million over-45s tune in to Radio 1. Three years ago, the average age was 29, just sneaking into its remit; now, supposedly, it's 32.

And the average for Chris Moyles's breakfast show is a year older than that. His 15-24 audience has fallen, while the 45-54 bracket has swelled. This 53-year-old finds the thought of Moyles in the morning a revolting prospect, but that's another story.

It might seem on first analysis odd for Moyles, 37 and three-quarters, to be hosting Radio 1's flagship show. Someone pushing 40 broadcasting to the nation's teens? Talk about talking down. But if the Radio 1 audience is slowly creeping towards middle age, then it makes sense. In fact, if the average age has gone up by three years since 2008, then that suggests it's simply holding steady.

Two years ago the BBC Trust was very specific, giving the then Radio 1 controller Andy Parfitt a clear command: target the teens. The station's executives were reported to be worried that some of their DJs were too old for the job. In this year's annual report, the trust repeated the message, saying it would "continue to challenge BBC management to ensure that Radio 1 focuses more clearly on younger listeners".

So does Parfitt's new successor Ben Cooper – who's just the wrong side of 40 – have a problem? GMG Radio's chief executive Stuart Taylor was keen to stick the boot in. "My message to Ben Cooper would be: You have got the job, now bring the station into line. What are you going to do to meet the trust's clear instructions? The trust has asked [Radio 1] to do something that they are patently not doing. The question is: what happens now? If Radio 1 was regulated by Ofcom and not the trust – if we were doing this – then it would be a breach of our licence and we would be taken off air."

Fighting talk. But then, he would say that, wouldn't he? GMG is home to Smooth Radio which, with its easy-listening melange of soul and R'n'B and its roster of such ex-BBC lags as Simon Bates and Kid Jensen, has most to lose from the incursion of Radio 1's greying demographic. Taylor suggests: "Why not redesign Radio 1 around 15- to 29-year-olds?" In other words, stay off GMG's turf.

The BBC wasn't going to take this lying down. "Radio 1's young audience has actually increased and now reaches... 45 per cent of all 15- to 24-year-olds in the UK." And what about Smooth Radio anyway? Are all their listeners over 30?

If Cooper does want to make his mark, though, and get down with the kids, he has history on his side. In the 1990s, new boy Matthew Bannister took not so much a new broom as a great big hatchet to the Smashie and Nicey brigade. A long list of erstwhile luminaries – Simon Bates, Dave Lee Travis, Alan Freeman, Bob Harris, Gary Davies, Steve Wright, Bruno Brookes, Johnnie Walker – either jumped or were pushed. And in 1995 Bannister banned "old" music – by which he meant five years and older – from the daytime playlist.

But apart from the fact that the BBC Trust might not be best pleased that its demands for Radio 1 to get down with the kids are apparently being ignored, should Cooper even be worried? The generations are crunching up; the music scene has never been more fragmented and niche-driven, but it's not necessarily fracturing along age lines.

That's not to say that eightysomethings and teenagers have the same tastes, but a 20-year-old and a 50-year-old might find they have more in common than they think: they might both like Coldplay and Mumford and Sons, Elbow and Madonna; they might well both watch Jools Holland on a Friday night and be comparing Noel Gallagher's new solo album with brother Liam's band Beady Eye.

My children like the Beatles, the Beach Boys and the Rolling Stones; I like Dizzee Rascal, Mark Ronson and Arctic Monkeys. My 18-year-old stepdaughter's current repeat-play favourite is Hendrix's "Hey Joe"; mine is "Black Hole" off the new Death in Vegas album. Back in 1967, when Tony Blackburn famously lowered the needle on to the Move's "Flowers in the Rain", Radio 1's first record, the generations were more clearly demarcated, and not just musically. There was a short, sharp transition from teendom to adulthood. Most twentysomethings would be married off or be dangerously close to it. Families were started younger, and if you weren't fixed up with a career and a home of your own by the time you were 30, questions would be asked.

Although Radios 1 and 2 shared plenty of airtime at the beginning, they had clearly distinct identities (though Radio 1 did have one or two oldies such as Jimmy Young and Pete Murray on board at the start). The Beatles might have appealed to all ages, but the Rolling Stones were the band you didn't want your daughter to marry. Next year Ol' Rubberlips and co take to the road to celebrate their golden jubilee – and you can bet that though there'll be legions of middle-aged spreads squeezing into T-shirts with a big tongue on the front, there'll be plenty of fit young things in attendance, too. Programmes like The X Factor appeal to all ages (bizarrely, in my book, but that's just me), and the all-round success of artists such as Adele, Duffy and Amy Winehouse suggests there's plenty of stuff around that crosses the generations. John Lewis is using the Smiths to sell their stuff, for goodness' sake. Heaven knows I'm saleable now.

The other reason that Cooper shouldn't be too concerned is the Mobo-orientated 1Xtra. The youngsters Radio 1 is missing out on are probably tuned in to that instead. If there is music to divide the generations these days, it's hip-hop, rap, grime and garage and all those other genres that most parents don't get. And the situation is further complicated by online streaming, Facebook recommendations and all the other platforms that make the idea of executive-imposed playlists redundant. I suspect that some teenagers hardly listen to the radio at all these days.

Those 32-year-olds the GMG man was going on about, even those 54-year-olds, are by and large, I suspect, listening to Radio 1 because that's what they've always done. It's a surefire bet that the 2.5 million over-45s were listening to Radio 1 30 years ago. It's probably a breakfast-time habit unbroken for decades, from Blackburn and Noel Edmonds, Mike Read, Steve Wright, Chris Evans and the rest, right through to Moyles. So in 20 years, will the average Radio 1 listener be drawing a pension? And if so, does it really matter?