Sign of the rhymes: People's poet Roger McGough tackles death and ageing but doesn't ditch the comedy

A riddle dances through my mind as I walk through the tranquil, tree-lined, sunlit streets of Barnes in south-west London, towards Roger McGough's house. "Try this for size:/ Figure out or forfeit the prize/ And here's the clue:/ Not a red herring, but a passe-partout/ In leisurely pursuit, Holmes excels/ Hercule exercises those little grey cells..." It is a typically playful poem from McGough's latest collection, That Awkward Age. All week I have been trying to solve it, and now, only a few doors away from his house, I confess myself defeated.

McGough answers the door promptly, with a smile and a rock-firm handshake. It is impossible to believe that he was born before the Second World War. He looks fit and in superb nick, wearing a pair of cool specs with transparent frames, a shirt as blue as the summer sky and a piratical earring. We sit at a table in his luxuriant arbour of a garden, under the shade of a pergola, our talk accompanied by the trilling of birds and the buzzing of innumerable bees.

McGough shot to fame in 1967 as one of the "Liverpool Poets" (the others being Brian Patten and Adrian Henri), whose joint collection, The Mersey Sound, remains one of the best-selling poetry collections of all time. How has his work developed since then?

"They were young man's poems. I was influenced by people such as ee cummings, and I had this habit of running words together – 'bitofalad', that sort of thing – and I was also influenced by beat poets such as Lawrence Ferlinghetti. It was more spontaneous, speaking straight to the reader. Not that I didn't work on them – I did – but now the poetry's more crafted. When you get to my age you're not sure how many more poems there are going to be, so you tend to hang on to them for longer."

It's noticeable that in the new collection there are more literary allusions than in the early work, with glances at Keats, TS Eliot and Rimbaud, among others. He smiles. "That's true, I like to drop those in occasionally... but some of the same themes are still there. I've always liked writing about ordinariness, about buses and chip shops and launderettes and that's still there. I'm writing more about ageing and death now, which is only to be expected, but that theme was there in the earlier work too." A good proportion of the poems in That Awkward Age do indeed speak of these themes, and often the treatment is humorous: "Wisdom Teeth" is a comic elegy to the loss of that "fabulous quartet", ending with the lines "I am become gobsmacked and ghoulish/ like an Edvard Munch"; "I Am Not Sleeping" is advice to attendees of McGough's funeral: "you are not here to celebrate/ but to mourn till it hurts".

"The humour comes in because it's a subject I'm scared about, and that's the way I deal with it. At least some of the time. In my earlier poems I'd seek refuge in comedy more often than I do now. When it started getting serious I had a tendency to veer off into a joke. Some of my work is a lot darker now." One of the most poignant poems is "Press Save", an almost Larkinesque vision of writing an elegy for a friend on Guy Fawkes night. It's one of the best poems in the collection. "That was written for a very good friend, [the actor, scriptwriter and author of McCarthy's Bar] Pete McCarthy, who I never thought would die before me. He was only in his fifties." Another of the more serious poems, "A Fine Romance", is an unflinching but tender look at the possibility of dementia – "Forgive me darling, in advance/ for the slow macabre dance/ I may one day lead you into" – and has been adopted by the Alzheimer's Society for a publicity campaign.

Still, it's probably true to say that McGough's muse inclines him to comedy more often than not. Many of the poems here could be characterised as light verse, and I don't mean that deprecatingly. I mean clever, funny, skilful light verse that delights the reader, with witty rhyme such as momento/ cento, ceilidh/ ukulele or Sartre/ Montmartre.

The poem "Larry David" is a complaint that people mistake McGough for the Amercian comedian; "Mistaken Identity" is a follow-up on the same theme which made me snort with laughter. "Love in the Launderette" displays McGough's talent for wordplay, with each couplet ending in a homophone; while "Macca's Trousers" recounts the tale of how a moth-eaten pair of Paul McCartney's trousers came to be displayed in the World Museum in Liverpool.

"I was in the pop group The Scaffold with Paul's brother, and he gave me this pair of trousers which Paul had handed down to him. I wore them a few times, then thought that maybe I should give them back. But after hanging them up at the back of the wardrobe, I forgot about them, and when I came across them years later the crotch area was peppered with moth-holes. I decided I couldn't really return them in that state, so I wrote a poem about them and donated it, with the trousers, to the World Museum. So if Paul wants them back he knows where to get them!"

The collection concludes with a group of comic monologues by the lesser-known husbands of famous women: there's Mr Blyton, Lord Godiva, Mr Sappho and Mr of Arc. "It's a nod to Carol Ann Duffy, who wrote poems based on the wives of famous men," he explains. I have to ask: his own name had been bruited as a possible candidate for Poet Laureate, so what did he think of Duffy's appointment?

"Oh, it's a very good appointment," he says decidedly. "I know her well and she'll be really good at the job. Her poetry's popular, it's accessible but it's got depth, she writes for children as well as adults, she'll be an excellent ambassador for poetry." All of those things would also have been true of McGough, of course. While we're on the subject of appointments, I can't resist enquiring what he thinks of the recent kerfuffle over the Oxford Professor of Poetry position (which was awarded to Ruth Padel after Derek Walcott was removed from the frame, only for Padel to resign when it emerged that she had forwarded information to journalists about charges of sexual harassment against Walcott). "I think it's a great shame," says McGough. "I can't see that Ruth did anything so very wrong – the information was already in the public domain. I can see why people love a tale of academic skulduggery, but the final outcome is that Ruth's been deprived of a position she deserved and would have been excellent in." But now the position's vacant again, would he consider it, if offered? "They haven't come knocking at my door yet! And no, I wouldn't take it on. I wouldn't have the time."

At an age when many people are content to take things easy, McGough is as busy as he's ever been. As well as presenting Radio 4's Poetry Please every week, he is dividing his time between London and Liverpool at the moment, working on the new production of Molière's The Hypochondriac, which he adapted and which opens this month at the Liverpool Playhouse. What attracted him to Molière?

"I was asked a couple of years ago to adapt Tartuffe, which I didn't want to do at first as I wasn't sure I'd be capable of it," he says with characteristic modesty. "But I had a go and I found it came quite naturally to write in rhyming couplets. So when I was asked to do Le Malade Imaginaire as a follow-up, I was happy to do it. When I started work on it I was away on a cruise – in fact I was working on a Saga holiday – and I didn't have the original with me, only a couple of translations. Both of these were in prose and I thought, 'That's a bit lazy, I'm going to do it in couplets like Molière!' It was only when I got back from the cruise that I got hold of the original and realised that Molière had actually written this one, unlike all his other comedies, in prose! But since I'd already done a good bit of it in rhyme by then, I decided to stick with it." We both laugh – something that happens a lot when you are in conversation with Roger McGough.

The time has come to ask him about the riddle. What can it be? Smiling, McGough talks me patiently through the poem, until the answer pops into my head. (Look away now if you don't want to know the answer...) In the ludic spirit typical of McGough the answer to all the clues is... clues.

The extract

That Awkward Age By Roger McGough Viking £12.99

O Lord, let me be a
burden on my children For long they've been
a burden on me. May they fetch and
carry, clean and scrub And do so cheerfully.
Let them take it in turns
at putting me up. Nice and sunny rooms
at the top of the stairs With a walk-in bath and
lift installed At great expense... Theirs

from 'Payback Time'