Television, the great medium of the late 20th century, simply will not be the same without the influence of Sir David Frost, who died on Sunday.

His spellbinding interrogation of Richard Nixon in 1977, the first after the President’s resignation over Watergate, was his career-defining moment – best characterised by his theatrical tossing aside of his clipboard of questions. It made his name in America and transformed the art of the broadcast interview.

But he was also a great pioneer of satirical comedy, electrifying a generation with new possibilities in puncturing those in power as the host of That Was The Week That Was in 1962. So influential was the show that the BBC dropped it over fears it might unduly sway the electorate.

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Sir David, who was 74 and died on board the Queen Elizabeth cruise ship where he was to give a speech, was not only a compelling figure on camera; he was a great strategic thinker within the broadcast industry who helped change the rhythm of television in 1983 as one of the co-founders of TV-am. His relationship with Al-Jazeera played a crucial part in establishing the reputation of the Qatar-owned network as a global news provider which challenges the hegemony of Western broadcasters.

David Cameron, who was due to be interviewed by Sir David this week, led the tributes to the broadcaster. “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.” He said Sir David was “both a friend and a fearsome interviewer”.

Tony Blair lamented the loss of a “huge figure in broadcasting” and 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 good-natured man.”

The broadcaster Jon Snow told The Independent: “Frostie was the first great current affairs showman. His style of interviewing was unparalleled: his ability to put guests at ease – often to the point that everything appeared so ridiculously laid back that many of his subjects would barely realise when the killer question had been delivered.”

“Television-wise, he was a breed apart: one driven guy who dared to chase the outrageously impossible.”

There were few world leaders who could resist the charm of an interview invitation from Sir David. His office was lined with photographs of him with the most powerful figures of his lifetime, including Bill Clinton and Mikhail Gorbachev.

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But Sir David’s own profile had grown as much as many of theirs, helped by the making of the 2008 film Frost/Nixon, which showed how he personally ensured those historic interviews took place despite a lack of backing from the major networks. The film’s director Ron Howard said: “He had the nerve to do this outrageous, ridiculous thing of bundling these local stations together and still create a mega television event and it worked.”

The writer of the film Peter Morgan said the “legendary broadcasting figure” had enjoyed an “extraordinary, four-dimensional, vivid career.”

Sir David’s famed conviviality had been part of his success in landing star guests from across the worlds of politics, sport and entertainment, throughout his career. The secret of his interviewing style – which prised from Nixon the admission that “I let down the country” – was to put people at their ease. Jealous critics dubbed his show “Bedtime with Frost”. But his friend and fellow broadcaster Sir Michael Parkinson said yesterday: “It’s not right to say he was a ‘soft’ interviewer – he had a persuasive interview style which led to the unmasking of a scoundrel.” Sir Michael added that “I never heard him say a bad word about anybody”.

Sir David’s move to Al-Jazeera risked his reputation in America. By 2011, Sir David so charmed the former Defence Secretary Donald Rumsfeld, who had previously dubbed the network as “vicious”, that he exclaimed: “I’m delighted you are doing what you are doing.”

British audiences will remember Sir David as a broadcaster of remarkable breadth. When That Was The Week That Was was dropped after one series, he fronted The Frost Report, which gave an early break to a generation of star British comedians including John Cleese and Ronnie Barker.

Cleese said on Sunday: “I owe a great deal of my professional career to David and I am very grateful for what he did for me. Life is going to feel rather diminished by the loss of his welcoming, cheery and optimistic voice.”