Connor moved on to the London
Old Vic Company for a 1947–48 season at the
New Theatre. His most notable performances there were as Chaplain de Stogumber in
Saint Joan and Dobchinsky in
The Government Inspector, which starred
Alec Guinness. Realising he was not a "tall, impressive juvenile lead or a young lover type", he decided to specialise in comedy. Connor appeared in
Talbot Rothwell's farce
Queen Elizabeth Slept Here in the
West End in 1949. He took over from
Peter Sellers in
Ted Ray's radio show ''
Ray's a Laugh'', which was launched by the BBC in 1949 as a successor to
Tommy Handley's
ITMA. Connor played the brother-in-law, and other oddball characters such as Sidney Mincing. Ray took Connor with him to his TV shows, and the pair would star together in the third
Carry On film,
Carry On Teacher. On occasion, he appeared in
The Goon Show, standing in for regular cast members struck down by illness. He also appeared in the anarchic, Goon-style TV series
The Idiot Weekly, Price 2d (1956) and
A Show Called Fred (1956). Connor gained a small role in the film
The Ladykillers (1955) as a taxi driver. In 1958, he was cast in the first
Carry On film,
Carry On Sergeant, and became one of the regular cast in the series, appearing in seventeen of the original thirty films and many of the associated television productions. Alongside
Kenneth Williams and
Eric Barker, Connor was one of only three actors to appear in both the first and last of the original sequence of
Carry On films (
Carry On Sergeant and
Carry On Emmannuelle). In his earlier
Carry On appearances, Connor frequently played the romantic lead or other sympathetic roles (typically with an element of comically neurotic anxiety), while later appearances saw him play less sympathetic characters such as married men with wandering eyes who made lascivious remarks. In
Carry On Nurse (1959), his real-life son Jeremy appeared as his character Bernie Bishop's son. In 1961, he starred with fellow
Carry On stars
Sid James and
Esma Cannon in the comedy film
What a Carve Up! In fact, in the 1959–61 period, he was one of the most prominent leading men in British comedy films. As well as
What a Carve Up! and the
Carry On films, other films he starred in during this period included
Watch Your Stern (1960),
Nearly a Nasty Accident (1961) and the
Dentist films. In 1960, he did the voices of the horse and dog in the
Four Feather Falls puppet series. Connor had a good tenor voice, which he occasionally used to good effect, such as in the 1962 movie
Carry On Cruising. In contrast with some of his
Carry On co-stars, Connor found further success on the London stage. He starred in the revue
One Over The Eight (1962), at the
Duke of York's Theatre, the original London West End production with
Frankie Howerd of the
Stephen Sondheim musical
A Funny Thing Happened on the Way to the Forum (1963), as Hysterium – and directed the show when it went on tour –
The Four Musketeers (1967), with
Harry Secombe at the
Theatre Royal, Drury Lane, playing King Louis XIII, and the revue
Carry On London (1973) at the
Victoria Palace. Between 1971 and 1973, Connor joined ''
Dad's Army stars Arthur Lowe and Ian Lavender in the BBC radio comedy Parsley Sidings. On television, he appeared in The Black and White Minstrel Show'', as Whatsisname Smith in the children's show
Rentaghost (1983–84), and as
Monsieur Alfonse in ''
'Allo 'Allo! (1984–1992) and Uncle Sammy Morris in Hi-de-Hi! (1986–88). He also made guest appearances in sitcoms including That's My Boy and You Rang, M'Lord? and he also appeared in the episode "Sense and Senility" of Blackadder the Third'' in 1987, alongside fellow veteran comic star
Hugh Paddick. In 1991, he was appointed Member of the
Order of the British Empire (MBE). Connor was still working just days before his death, appearing on ''
Noel Edmonds'
Telly Addicts. His final TV appearance, as Mr Warren in The Memoirs of Sherlock Holmes episode The Red Circle'', was broadcast posthumously in 1994. ==Death==