An army officer's son, Kydd was born to English parents in Belfast, Northern Ireland, and moved back to London as a child. He was educated at Dunstable Grammar School in Dunstable, Bedfordshire. During the mid-1930s Kydd was an MC for various big bands such as the Oscar Rabin Band. He would warm up audiences with jokes and impressions and even some tap dance routines then introduce the other Singers and attractions on the bill. During the late 1930s he had joined the Territorial Army serving with the Queen Victoria's Rifles and when war broke out he was called up for active Service.

Kydd took part in more than 200 films and 1,000 TV plays and series including, The Adventures of Robin Hood, The Pickwick Papers, Mess Mates, Arthur Askey, Benny Hill, Charlie Drake, Harry Worth, The Expert, Dixon of Dock Green, Crane and Orlando in 1963. In Crane, Kydd had appeared as the lovable smuggler Orlando O'Connor. The programme starred Patrick Allen, as a Briton who moved to Morocco to run a cafe and had an aversion to smuggling. Kydd's character was so popular that when 'Crane' finished he was given his own programme, Orlando, a children's adventure series.

He also appeared in the Fossett Saga, and Curry and Chips, as well as the big-screen versions of Dad's Army and Till Death Us Do Part. Amongst his many television appearances were The Tony Hancock Show, critically acclaimed series Minder, Crossroads, Coronation Street (playing the part of Mike Baldwin's father, Frankie), The Eric Sykes Show, and Follyfoot. In 1974, Kydd played the part of a cabbie in Thames Television's A Dickens of a Christmas.