In the late 1960s, when television was an exciting and reliably star-making medium, there was one show everyone wanted to be on: Play School. The ABC staple aired twice a day every weekday, making it a huge platform for any presenter. So when Don Spencer was offered a spot on the children’s program in 1968, everything changed.

“I couldn’t go anywhere without being recognised,” the now 89-year-old recalls. “I couldn’t walk into a shop. I couldn’t get on to an airplane. I went to a rugby union [game] and half the crowd turned around and sang one of my songs to me. It’s ridiculous. But it just kept going, so I just kept going with it.”

That’s something of an understatement. Spencer logged 30 years of service with Play School in Australia, and 17 on the English version that aired concurrently, becoming as much a part of the fabric of the show as Big Ted and the Rocket Clock. It was such a dream gig that Spencer never considered it a job at all.

“Honestly, it was a beautiful show to work on. We all got along great,” he says. “I pity the actors who play murderers in films because people must think they are like that. But people always come up to me and go, ‘oh, Play School! I likey’”.

It may be what he’s best known for, but Play School was just one chapter of Spencer’s career. He had an early stint as a mainstream pop singer, rubbing shoulders with the Beatles at Abbey Road (“they’re good guys”) and touring with the Rolling Stones. He hosted a radio show on the BBC, where he entertained guests such as Dustin Hoffman and Meryl Streep. He tried his hand at acting, appearing on shows including Sons and Daughters and A Country Practice.

And long before the Wiggles ever started juggling hot potatoes, Spencer released 16 albums of children’s songs, earning an Order of Australia in 2007 for his contributions. The biggest of them was Feathers, Fur or Fins, which turned 40 this year and remains burrowed in the subconscious of generations of Australians thanks to tunes like Bob the Kelpie and Please Don’t Call Me a Koala Bear (“cos I’m not a bear at all”, as the chorus unforgettably goes).

“I don’t know where the 40 years has gone,” Spencer says, who is as sharp as ever, full of anecdotes about the media landscape of the 60s and happy to wax lyrical about the powers of children’s music (“Music is magic!” he says).

We’re sitting in his Darlinghurst apartment, looking out at the panoramic view of Sydney Harbour, a vista he says he never gets sick of. It’s a long way from where he started. Spencer says he felt inspired to make children’s music because of his “very challenging” childhood in 1940s Tamworth. He grew up witnessing domestic violence and frequently ran away from home, but always found solace in music. “I always thought there’d be other kids out there that music could help,” he says.

Spencer left Australia in 1957, working his way around the world doing odd jobs before landing in the UK and recording demos of a few songs he’d written on the road – one of which is 1963’s Fireball XL5, which to his surprise reached 32 in the UK charts. “Then suddenly I was a pop singer,” he says. Many doors opened but Spencer always contended with a degree of impostor syndrome (“Somebody would say there’s an eight-bar intro, but the only bar I knew was where I got a drink. That’s how little I knew about music.”) He regards the brilliant career that followed as accidental – albeit one he’s “still accidentally carrying on in my 65th year”.

Decorating his walls are memories of exactly where that career took him: everything from a signed photo of Doris Day (“she was my heroine and I got to meet her”) to a snap of David Bowie with his daughter, singer-songwriter Danielle Spencer (formerly married to Russell Crowe). There is also a newspaper cutting of a group of BBC Radio presenters; Spencer is huddled next to Cilla Black, Tony Bennett and – awkwardly – Rolf Harris. (“To be honest I quite got on with Rolf; I had no idea about the terrible things he did,” he says). There are pictures of him and former Play School colleague Benita Collings on set; family photos of his kids and grandkids. Often, at night, he’ll look over the photos with a glass of wine and “let them take me away”, he says.

“I don’t want to name drop too much but I was lucky enough to meet people I never in my life dreamt I’d meet, as a kid living in Tamworth,” he says.

After establishing his career in the UK, Spencer married and moved back to Australia to raise his children. That was when he was offered the spot on Play School. The trick to doing that job well, he feels, was simple: pretend you’re speaking to just one kid, and don’t condescend.

“My voice doesn’t change. I never do this bloody talking down to kids business, you know – ‘Hello, darling’,” he says, affecting a cutesy voice with the roll of an eye.

Spencer recorded Feathers, Fur or Fins in 1985 because he wanted to rectify the fact that there were virtually no children’s songs about Australia, even on Play School. The ABC issued an anniversary rerelease of the album this month, with each song reimagined by a different contemporary artist, including the Whitlams’ Tim Freedman and the ex-Wiggle Emma (Memma) Watkins, who covers Sh-Sh-Sugar Glider.

Watkins grew up dancing to Spencer’s music at preschool and now appreciates his work in a different light. “Songwriting in the children’s space is sometimes not taken that seriously, but it really takes a lot of depth and research and understanding to know when a song is right for a preschooler,” she says. “And Don always had that knack, which is why his music is so beloved.”

Given he is only months away from his 90th birthday, you could be mistaken for thinking that Spencer is retired, or that he regards this Feathers, Fur or Fins reissue as his last release.

“I’ve still got a recording contract” he says. “Taylor Swift is not losing any sleep over me, but I am still writing my little songs.”

And he still responds to his fans. He gets messages weekly, from fans in Kempsey to Kentucky, who grew up listening to his music and want to say thanks. Spencer diligently answers every single one, often sending back videos of himself singing happy birthday on request.

Spencer says it has been “an honour” to be part of so many childhoods, but that he would like his legacy to be the Australian Children’s Music Foundation, the charity he founded in 2002, which provides music programs and free instruments to disadvantaged schools and youth justice centres. Music, he feels, inspires creativity and imagination; offering children joy and hope. “And if you don’t have hope, you have no future,” he says.

“If I’ve contributed to that, that’s better than anything else I’ve ever done.”

• The 40th anniversary edition of Feathers, Fur or Fins is out now via ABC Music