Sir David Frost, the journalist and broadcaster whose lengthy career stretched from cutting-edge 60s satire to heavyweight interviews and celebrity gameshows, has died of a heart attack on a cruise ship, his family said.

The 74-year-old, whose programmes included That Was The Week That Was and The Frost Report, was to have given a lecture on board the Queen Elizabeth, which had just set sail on a Mediterranean cruise.

Frost boarded the ship at Southampton on Saturday afternoon, and had been due to speak to passengers en route to Lisbon.

Frost, who was knighted in 1993, helped establish London Weekend Television and TV-am. He was famed for his political interviews, most notably with Richard Nixon in 1977, in which the US president conceded some fault over Watergate for the first time.

A family statement said: "Sir David Frost died of a heart attack last night aboard the Queen Elizabeth where he was giving a speech.

"His family are devastated and ask for privacy at this difficult time. A family funeral will be held in the near future and details of a memorial service will be announced in due course."

David Frost and Richard Nixon in April 1977. Photograph: John Bryson/Time & Life Pictures/Getty Image

David Cameron, who sent a tweet of condolence, released a statement expressing his sympathies to Frost's widow, Carina, and his wider family.

He said: "Sir David was an extraordinary man – with charm, wit, talent, intelligence and warmth in equal measure. He made a huge impact on television and politics. The Nixon interviews were among the great broadcast moments, but there were many other brilliant interviews. He could be, and certainly was with me, both a friend and a fearsome interviewer."

Michael Grade, who knew and worked with Frost for more than 30 years, called him "a huge figure in the history of British broadcasting".

Grade told the Guardian: "He was the first real superstar of the screen who was purely and simply a product of television. Secondly, he had an amazing business skill. He was a performer, a journalist, an impresario and an entrepreneur. That's given to very, very few people."

Grade added: "He was kind of a television renaissance man. He could put his hand to anything. He could turn over Richard Nixon or he could win the comedy prize at the Montreux Golden Rose festival. It was just extraordinary."

Peter Jay, who founded TV-am alongside Frost, told BBC News: "On the screen he was a very talented and original performer, but it was his talent off-screen, his quality as a human being, his capacity for friendship and loyalty, that were in my opinion the thing that raised him to quite an exceptional level."

David Frost in 1964. Photograph: George Konig/Rex Features

Greg Dyke, the former BBC director general who worked with Frost, rescuing the initially struggling TV-am, described him as "a great, great friend". He said: "He understood the whole breadth of television, so he wasn't just a news and current affairs man, he could also be an entertainment man, so he knew it all."

Loyd Grossman, who worked with Frost on TV-am and then on the long-running ITV gameshow Through the Keyhole, called him irreplaceable.

Grossman told Sky News: "He was almost the most variously talented journalist in British broadcasting history. His loss will be immense to all of us. He was also an incredibly generous broadcaster to work with."

Other tributes stressed the same point, that Frost's sometimes mocked and seemingly cosy interviewing style was in fact one of his strongest attributes.

Tony Blair said: "He had an extraordinary ability to draw out the interviewee, knew exactly where the real story lay and how to get at it, and was also a thoroughly kind and good-natured man. Being interviewed by him was always a pleasure, but also you knew that there would be multiple stories the next day arising from it."

Sir Michael Parkinson, a friend for 40 years, said Frost was "an extraordinary guy". He said: "When you think of all the stuff he was responsible for, never mind the Nixon interview and the two television companies he helped set up too, it's remarkable.

"But it's not right to say he was a 'soft' interviewer. He had a totally persuasive interview style which led to the unmasking of a scoundrel."

In a Guardian interview in 2008, Frost discussed his style. "I think there's a danger when you adopt an immediately hostile position without having the goods, without having the smoking gun. I think that's a real mistake," he said. "You shut people up instead of opening them up. You can ask just as tough a question in a softly spoken way."

Sir David Frost in 1966 on The Frost Programme. Photograph: ITV/Rex Features

Blair was among an unbroken line of British prime ministers from Wilson to Cameron interviewed by Frost. Frost interviewed every US president from Nixon to George W Bush.

The Kent-born son of a Methodist minister, Frost turned down a possible football contract with Nottingham Forest to attend Cambridge University, where he was active in student journalism and secretary of the Footlights theatrical revue. From there he became a trainee at independent television before finding fame as the host of That Was The Week That Was, the pioneering TV political satire show.

The programme ran on the BBC during 1962 and 1963, before being cancelled over worries it could unduly influence an upcoming general election. Frost then hosted a US version.

From then on, Frost was a regular TV figure on both sides of the Atlantic, with shows including The Frost Report and Not So Much a Programme, More a Way of Life. Frost's distinctive delivery of his catchphrase, "Hello, good evening and welcome," became instantly recognisable and much mocked.

In later years, Frost hosted the Frost on Sunday talkshow on ITV, before returning to the BBC in 1993 for the first time since the early 1960s for Breakfast with Frost, which ran until 2005.

For many years he also hosted Through the Keyhole, which by coincidence returned to ITV on Saturday night in a revamped format.

After Breakfast with Frost ended, the broadcaster made a surprise move to al-Jazeera, where he interviewed political figures.