Here's a measure of Rolf Harris's popularity. Whenever the genial, bearded Aussie appears on Animal Hospital, pet dogs in front rooms up and down the country start barking and licking the television-screen with excitement. And there's video evidence to prove it. So Harris is not only a hit with 10 million-odd humans every week, but with much of the animal kingdom, too.

In this ironic age when so many presenters come with in-built quotation- marks, Harris possesses a refreshing innocence. His unfeigned, old-fashioned sense of enthusiasm comes as a relief in an era when cynicism is the coolest thing in Britannia. It would be hard, for instance, to fake the way he so regularly chokes back the tears on Animal Hospital. In his new Sunday BBC1 show, Rolf's Amazing World of Animals, he chuckles unself-consciously to himself as he feeds milk to a tiny hedgehog. "Isn't it beautiful? How can people ill-treat these little things?" He wouldn't know what post- modernism was if it escaped from its cage and bit him.

"Rolf is a genuine person," according to Dale Templar, the series producer on Rolf's Amazing World of Animals. "He has a great feelgood factor. A lot of people say to me, `Rolf is my idea of the ideal uncle'."

Conforming exactly to that image, Uncle Rolf chimes in. "I've always tried to be honest on screen, and never con people or use them for my own glory. People say `never work with children or animals', but that only applies if you want to be a big star. On my programmes, at every turn the audience will be watching the child or the animal, so I'm happy to step back and let them take the limelight. If they're doing something fascinating, you should get out of the way." This may all sound sickeningly modest, but it is that very anti-stardom which, perversely, makes him such a star.

A grinning, livewire presence in a natty, untucked turquoise shirt, Harris is liable to burst into song at any given moment. This infectious lust for life is just one reason why he has become the biggest cult this side of Teletubbies. Youngsters are drawn to the man who first appealed to their parents' generation in the 1960s, crooning novelty hits such as "Tie Me Kangaroo Down Sport", "Jake the Peg" and "Two Little Boys" and using his bonhomie to shift products such as the Stylophone.

Virtually every student union in the land now boasts a Rolf Harris Appreciation Society - "I turned up uninvited at a Society meeting in north London once, and they nearly died of fright". Fans attend his gigs with "tribute" false beards, glasses and wobble-boards. When he first played Glastonbury in 1994 - he has since became something of an institution there and was voted the festival's Best Ever Performer - "I walked out and everyone chanted `one Rolfy Harris, there's only one Rolfy Harris'. Then 80,000 people sang every word of every song for the next hour and a half. I sang "Sun Arise" out of key, but I never realised at the time because I couldn't hear the band. When I went off, they shouted `we want Rolf' for 10 minutes. I suppose they like me because at my shows there's entertainment involved. Most people in rock'n'roll just say `here's another song'. They sing at the audience rather than to them. They think that volume equates with entertainment, and it doesn't."

On the back of his early chart hits in the 1960s, Harris went on to host his own TV shows with such dodgy titles as Rolf's Walkabout, Rolf on Saturday, OK?, Hey Presto, It's Rolf, and Rolf's Here! OK? On these, he tended to specialise in humming didgeridoo-type tunes while splashing emulsion on a canvas and asking "Can you tell what it is yet?"

Despite this, 38 per cent of people polled in a 1992 survey had him ahead of Rembrandt, Van Gogh et al as "the world's most famous artist". He reckons that painting is "a form of magic. That line wasn't there a minute ago, and when it turns out to be something you weren't able to suss out, it's wonderful."

After a period in the doldrums during the 1980s, Harris's career was re-born in the early 1990s, thanks to the most unlikely vehicle: his wobble- board version of the Led Zeppelin hard-rock standard, "Stairway to Heaven". "At first when people heard I was recording that, it was `shock horror, somebody's mucking about with our song'. Then people realised that I'd actually made it accessible to the ordinary bloke with all that `altogether now' stuff on the chorus. It was done with love and affection, rather than as a snide take-off. That song relaunched me because it finally gave people permission to say that they liked Rolf Harris. Before that, it would have been square to own up to it. But it's been amazing at this time of life to have another career thrust on you."

For all that, a suspicion remains that not all the reverence towards Harris is entirely straight-faced. There is the whiff of the mickey-take about some people's professed adoration of the Rolfster (pace, Mrs Merton).

Harris, however, is unruffled by ribbers. "I can take mockery. I don't mind people having a go at me. At least people know you're still alive. Anyway, I take all this stardom business with a grain of salt. The important thing is to mock yourself and know that it's all a big joke. You have to join in with the fun at your expense. But of course, if audiences don't immediately start singing `there's only one Rolfy Harris', I prompt them into it," he adds with a twinkle.

Now 68, Harris claims never to have been busier, and he shows no signs of slowing down. Templar hopes he will do more animal shows - "he's a real-life Dr Doolittle, a man who seems as if he can talk to the animals."

But she also foresees even bigger and better things for the man who has already been commemorated by a plaque on the street in Perth, Australia where he grew up. "What will be his next incarnation?" Templar wonders. "It would be interesting to see Rolf host a chat-show. Like Des O'Connor, he has a very nice, relaxed feel. I think I'll speak to his agent..."

`Rolf's Amazing World of Animals' starts Sun 24 May on BBC1