The actor Peter O'Toole who found stardom in David Lean's masterpiece Lawrence of Arabia, has died aged 81, his family has annouced.

The acclaimed leading man who overcame stomach cancer in the 1970s passed away at the Wellington hospital in London following a long illness.

His daughter Kate O'Toole said: "His family are very appreciative and completely overwhelmed by the outpouring of real love and affection being expressed towards him, and to us, during this unhappy time. Thank you all, from the bottom of our hearts."

O'Toole announced last year he was stopping acting saying: "I bid the profession a dry-eyed and profoundly grateful farewell."

He said his career on stage and screen fulfilled him emotionally and financially, bringing him together "with fine people, good companions with whom I've shared the inevitable lot of all actors: flops and hits."

The president of Ireland, Michael Higgins, was among the first to pay tribute: "Ireland, and the world, has lost one of the giants of film and theatre."

"In a long list of leading roles on stage and in film, Peter brought an extraordinary standard to bear as an actor," Higgins said. "He had a deep interest in literature and a love of Shakespearean sonnets in particular. While he was nominated as best actor for an Oscar eight times, and received a special Oscar from his peers for his contribution to film, he was deeply committed to the stage. Those who saw him play leading roles on the screen from Lawrence in 1962, or through the role of Henry II in Becket, and The Lion in Winter, or through the dozens of films, will recognise a lifetime devoted to the artform of the camera.

Higgins, who knew O'Toole as a friend since 1969, said "all of us who knew him in the west will miss his warm humour and generous friendship.

"He was unsurpassed for the grace he brought to every performance on and off the stage," he said.

The British prime minister, David Cameron, paid tribute to the actor, saying that Lawrence of Arabia, his favourite film, was "stunning".

O'Toole's agent, Steve Kenis, said: "He was one of a kind in the very best sense and a giant in his field."

The O'Toole family announced there will be "a memorial filled with song and good cheer, as he would have wished", but until then they would like to be allowed to grieve privately.

Early in his career O'Toole became emblematic of a new breed of hard-drinking Hollywood hellraiser.

"We heralded the '60s," he once said. "Me, [Richard] Burton, Richard Harris; we did in public what everyone else did in private then, and does for show now. We drank in public, we knew about pot."

In the 1990s he found stage fame starring in Keith Waterhouse's play, Jeffrey Bernard is Unwell, about a hard-drinking journalist who propped up bars in Soho. O'Toole's version sold out the Old Vic theatre in 1999.

Last month it was reported he had been coaxed out of retirement to act in a film about ancient Rome called Katherine of Alexandria in which he would play Cornelius Gallus, a palace orator. It is believed he completed filming on the project alongside Joss Ackland, Steven Berkoff and Edward Fox and the movie is due to be released next year.

O'Toole is believed to have been born in Connemara in County Galway in Ireland, and lived in London. He shot to stardom in the 1962 film of TE Lawrence's life story and went on to take leading roles in Goodbye Mr Chips, The Ruling Class, The Stunt Man and My Favourite Year. He received eight Oscar nominations and no wins – an unassailed record – though he was given an honorary Oscar in 2003. He considered turning it down and asking the Academy to hold off until he was 80, on the basis that "I am still in the game and might win the bugger outright."

He finally accepted, saying: "Always a bridesmaid, never a bride, my foot".

He is survived by his two daughters, Pat and Kate O'Toole, from his marriage to actress Siân Phillips, and his son, Lorcan O'Toole, by Karen Brown.

• This article was amended on 18 December 2013 to clarify Peter O'Toole's record of Oscar nominations.

More on Peter O'Toole

•Obituary: Peter O'Toole, 1932-2013

• Peter O'Toole: last of the 60s hellraisers

• Peter O'Toole: a career in clips