Ray Galton, one half of Galton and Simpson, the writing team regularly voted the funniest in sitcom history, has died at the age of 88.

The scriptwriter died “peacefully” on Friday night after a “long and heartbreaking battle with dementia”, his family has said.

Born in Paddington, London, Galton worked throughout his 60-year career with Alan Simpson, who died in February last year, aged 87. Most famously, they created Hancock’s Half Hour, the radio and television comedy that established Tony Hancock as the quintessential disappointed British antihero of the postwar years.

Many of the catchphrases they gave “the lad himself” were soon to enter into the English language, such as his aggravated “Stone me!”. The success of the Hancock show, which ran first on radio and later on television from 1954 to 1961, saw Galton and Simpson regularly hailed as the creators of situation comedy.

The duo also went on to create rag and bone men Steptoe and Son, the squabbling father and son of the landmark television series. This show, starring Harry H Corbett and Wilfrid Brambell, ran for eight series until 1972. At its peak, it commanded an audience of 28 million viewers.

Tessa Le Bars, Galton’s manager, said: “I have had the great honour of working with Ray for over 50 years and for the last 40 as his manager and friend. With his lifelong co-writer, the late Alan Simpson, they were regarded as the fathers and creators of British sitcom.”

The comedian Adrian Edmondson tweeted:

Adrian Edmondson (@AdrianEdmondson) Galton and Simpson were the masters. And also very kind - they never sued Rik and I for basically doing a pale copy of Steptoe & Son and Hancock’s Half Hour, and just adding a bit of mindless violence.

David Walliams tweeted:

David Walliams (@davidwalliams) What an incredible body of work Ray Galton has left us with. Some of the greatest TV comedy ever written, ‘Hancock’ & ‘Steptoe & Son’ are still the gold standard of sitcoms. Matt & I got to spend time with him & Alan Simpson. I was in complete & utter awe. https://t.co/g4JmvXPwUy

When he received the entertainment industry’s most prestigious award, a Bafta fellowship, in 2016, Galton’s speech referenced several of their greatest scriptwriting triumphs, including the most famous episodes of Hancock’s Half Hour, The Radio Ham and The Blood Donor: “We are happy and honoured to accept this award on behalf of all the blood donors, test pilots, radio hams and rag and bone men of the 20th century, without whom we would probably be out of a job,” he said.

Working together for more than 60 years, the writers met while they were being treated for tuberculosis at the same Surrey sanatorium in 1949. He and Simpson wrote to Frank Muir and Denis Norden, the leading comedy writers of the day, and were invited to the BBC’s Broadcasting House for a “chat”. They went on to write for numerous stars, including Frankie Howerd and Les Dawson.

But their most important creative moment undoubtedly came when they were still in their 20s. On 2 November 1954, the 30-year-old Hancock stood behind a radio microphone for the first episode of a new show, his first starring vehicle for the BBC radio.

Seven years later, Hancock was the most famous performer in Britain, winning 20 million listeners. His broadcast alter ego, Anthony Aloysius St John Hancock, resident of 23 Railway Cuttings, East Cheam, was a version of himself, but dressed like an old-fashioned dandy and full of delusions of grandeur. The show was first broadcast on BBC Radio from 1954 to 1959 and moved to BBC television from 1956. Regular performers included Sid James, Hugh Paddick, Hattie Jacques and Kenneth Williams.

Speaking in 1997, before the launch of new sitcom about his time as a youth in a sanatorium, Galton said: “Finding the plots used to be lot easier for me than the writing. Nowadays, I find the ideas much more difficult. Practically everything has been done.”

• This article was amended on 8 October 2018 to remove a misattributed quote.