Clive James, the broadcaster, poet and television critic, has died aged 80 after a long illness.

The Australian died at his home in Cambridge on Sunday, his agent confirmed. A private funeral attended by family and close friends took place in the chapel at Pembroke College, Cambridge, on Wednesday afternoon.

United Agents said: “Clive died almost 10 years after his first terminal diagnosis, and one month after he laid down his pen for the last time. He endured his ever-multiplying illnesses with patience and good humour, knowing until the last moment that he had experienced more than his fair share of this ‘great, good world’.

“He was grateful to the staff at Addenbrooke’s hospital for their care and kindness, which unexpectedly allowed him so much extra time. His family would like to thank the nurses of the Arthur Rank Hospice at Home team for their help in his last days, which allowed him to die peacefully and at home, surrounded by his family and his books.”

Don Paterson, James’s poetry editor at Picador, said: “Although it was hardly unexpected, it was still a shock to hear of Clive’s passing; despite his frailty in his later years, his life-force seemed almost indestructible … he was unfailingly warm, kind and hilarious company right to the end, and we’ll miss him terribly.”

Model Jerry Hall and Clive James at the Bafta awards in 1990. Photograph: PA/PA Wire/PA Images

Born Vivian James in Sydney in 1939, he studied at the University of Sydney before moving to London at the start of the 1960s. He later attended Pembroke College, Cambridge, where he was president of the Cambridge Footlights drama society and mixed with the likes of Germaine Greer.

He began writing criticism for literary magazines, before becoming the Observer’s television critic in 1972. There, his deadpan tone made for a markedly new approach to reviewing programmes; he later said he became unpopular in the office for laughing out loud at his own jokes while writing. At the same time, he developed a reputation as a poet, publishing satirical verse about politics and London’s literary landscape, and later as a memoirist, penning a series of autobiographies detailing his childhood in Australia and his move to England. His writing about television led to him stepping in front of the cameras in shows including ITV’s Clive James on Television.

He was unfailingly warm, kind and hilarious company right to the end Don Paterson

After decades of writing and broadcasting, he was diagnosed with cancer in 2010, resulting in a lengthy period of treatment. While continuing to write columns, James regularly predicted his own imminent demise. In 2014, he published the acclaimed valedictory poem Japanese Maple, which many took as a sign of his impending death. James said he had “confidently stated that when the maple tree in my garden turned to flame in autumn, that would be the end of me”, but he had been left in the awkward situation when “the tree turned red and I was still here, steadily turning red myself as I realised that I had written myself into a corner”.

He decided to make the most of the situation, spending two years writing the Reports of My Death column for the Guardian, in which he ruminated on what it meant to be approaching the end of one’s life.

Clive James pictured at London Weekend television in 1981. Photograph: Mirrorpix/Getty Images

On his website he gave advice to journalists and editors writing his obituary, telling them to keep in mind that when it comes to biographical details they should be aware “shorter is better, and that a single line is best”. He pledged to ensure his biography was up to date before he died: “I will keep updating it until they carry me to the slab, during which journey I will try to give details of my final medication.”

According to this account, a long and ultimately unsuccessful operation to remove a cancer on his cheek in February 2019 left him frail and almost blind in his final months.

James spent the spring and summer of 2019 writing and editing an autobiographical anthology called The Fire of Joy, which was finished a month ago and will be published in 2020. Paterson described it as “a pretty typical of his generosity that the last book Clive finished was a work of straightforward enthusiasm, a reader’s guide to his favourite poems”.

He married the academic Prue Shaw in 1968, and they had two daughters: Claerwen, a molecular biologist turned painter, and Lucinda, a civil servant and “world expert on CSI: Miami”.