Ronald Chesney, who has died aged 97, was one half of a comedy duo known as “the two Ronnies” before Barker and Corbett launched themselves as a TV double act with that name. Chesney and Ronald Wolfe worked behind the cameras, scripting two of the most popular sitcoms of all time, The Rag Trade and On the Buses, both set in the workplace and with a bawdy humour not always appreciated by TV critics but lapped up by millions of viewers. Chesney also had the distinction of being Britain’s most famous harmonica player in the years after the second world war.

“Everybody out!” was the catchphrase from Fenner Fashions’ militant shop steward Paddy, played by Miriam Karlin, in The Rag Trade (1961-63). It caught the imagination of a nation that was putting the austerity of the war years behind it and beginning to question the establishment. The programme came in the wake of the Boulting brothers’ 1959 trade union-versus-management film satire I’m All Right Jack.

Paddy was pitted against the dressmaking workshop boss, Mr Fenner (Peter Jones), and his foreman, Reg (Reg Varney), while the seamstresses – played by a cast that included Barbara Windsor and Sheila Hancock – had all the best put-downs. Karlin and Jones reprised their roles for a popular but short-lived revival a decade later (1977-78).

By then, Chesney and Wolfe had enjoyed even bigger success with On the Buses (1969-73), which regularly attracted up to 20 million viewers over its 73 episodes and seven series. “Get that bus out!” was one of several catchphrases uttered by Stephen Lewis as Inspector Blake, trying to keep the Luxton Bus Company on the road.

Varney starred as Stan Butler, chirpy driver of the No 11, with Bob Grant as his conductor, Jack, and both spent much of their time chatting up women. “I ’ate you” and “I’ve got you this time, Butler!” was how the miserable Blakey reacted to the various goings-on.

The sitcom’s astonishing popularity led to three spin-off films, On the Buses (1971) – the British box office’s biggest hit of the year – Mutiny on the Buses (1972) and Holiday on the Buses (1973), all of which Chesney and Wolfe produced, and its format was sold to the US as Lotsa Luck (1973-74).

Chesney was born René Cadier in London to French parents, Marius, a silk trader, and Jeanne (nee Basset). As a child, he learned the piano, but his career choice was influenced by a toy mouth-organ placed in his Christmas stocking one year, along with hearing Larry Adler playing the chromatic harmonica (one with a button-activated sliding bar), which led him to buy his own.

On leaving London’s French Lycée school at 16, he became a professional harmonica player, anglicising his name to Ronald Chesney, and established himself as a virtuoso when he toured ABC cinemas to perform between films. He made his radio debut on the BBC National Programme’s Palace of Varieties in 1937 and played in many other such shows, eventually combining classical music with Gershwin, Cole Porter and even boogie.

Exempted from serving in the forces during the second world war after having a TB-infected kidney removed, Chesney played his part by teaching musical skills to the troops and other listeners in the radio programme Let’s Play the Mouth-Organ (1940). His own eponymously titled show followed in 1941 and 1947, along with long runs in the radio series Variety Band-Box (1944- 51) and Workers’ Playtime (1949-56).

He also performed in concert halls around the world and released many records, including a show-stopping rendition of Rimsky-Korsakov’s The Flight of the Bumble Bee played at lightning speed. In 1951, he became president of the Hohner Harmonica Song Band League, which shortly afterwards became the National Harmonica League.

While providing musical interludes with his “talking harmonica” during the entire run of the radio comedy Educating Archie (1950-60), featuring the ventriloquist Peter Brough and his doll, Chesney met Wolfe, who joined the show as a scriptwriter in 1955. They teamed up and, with Marty Feldman, wrote for the final two series, as well as a TV version (1958-59).

When Feldman left to team up with Barry Took, Chesney and Wolfe continued together – Chesney giving up his career as a harmonica player – and created the 1961 radio sitcom It’s a Deal, starring Sid James as a bungling property developer.

The Rag Trade began 20 years of hit comedies for the pair on television: Meet the Wife (1963-66), starring Thora Hird; The Bed-Sit Girl (1965-66), with Sheila Hancock; Sorry I’m Single (1967), featuring Derek Nimmo; Wild, Wild Women (1968-69), including Windsor and Pat Coombs in a variation on The Rag Trade set in a millinery; Arthur Mullard and Queenie Watts in a caravan in Romany Jones (1972-75), then in a council house in Yus My Dear (1976); Lewis’s Blakey from On the Buses retiring to Spain in Don’t Drink the Water (1974-75); and John Inman playing a secretary in Take a Letter Mr Jones (1981).

They also wrote a 1989 episode of ’Allo ’Allo and Fredrikssons Fabrikk (1990-93), the Norwegian television version of The Rag Trade, as well as its 1994 film spin-off.

Chesney is survived by his wife, Patricia (nee Martin), whom he married in 1947, and their children, Marianne and Michael.

• Ronald Chesney (René Lucien Cadier), writer and harmonica player, born 4 May 1920; died 12 April 2018