Faulds was born to missionary parents in Isoko, Tanganyika. He married Bunty Whitfield in 1945. During the Second World War he served in both the Royal Air Force and the Fleet Air Arm.
After graduating from the University of Glasgow, he joined the Royal Shakespeare Company in 1948. However, he first came to a wider public recognition playing Jet Morgan in Charles Chilton's radio drama Journey into Space on the BBC Light Programme.
In 1959, Faulds and his wife played host to Paul Robeson, who had travelled to Britain to appear at the Royal Shakespeare Theatre, Stratford-upon-Avon in Tony Richardson's production of Othello. Robeson had only recently been permitted again to travel abroad, following the revocation of his passport. During this visit, Robeson inspired Faulds to take up political activism.
Faulds maintained his acting career throughout the 1960s and 1970s, and in particular became a key part of film director Ken Russell's repertory company, appearing in, among other films, Dante's Inferno (1967) (as William Morris), The Devils (1971), Mahler (1974) and Lisztomania (1975). Notably, he appeared in Russell's film The Music Lovers (1970) alongside Glenda Jackson, who like him went on to become a Labour MP.
One of Faulds' best-remembered roles is Phalerus in Jason and the Argonauts (1963), in which he took part in the skeleton fight scene that featured model work by Ray Harryhausen. Another was in "The Radio Ham" (1961), an episode of Hancock, as the unseen voice of 'mayday'.
Faulds first stood for Parliament as the Labour candidate in the 1963 Stratford by-election, caused by the resignation of John Profumo over a security scandal. He fought the constituency again in the general election the following year, but on both occasions he was beaten by the Conservative future Cabinet minister Angus Maude.
Also in the 1964 general election, the Labour Shadow Foreign Secretary, Patrick Gordon Walker, was defeated in controversial circumstances in the Smethwick constituency by Conservative candidate Peter Griffiths. Smethwick had become the home of immigrants from the Commonwealth in the years following the Second World War, and Griffiths' 1964 campaign was critical of Conservative government policy as well as of Labour statements on the issue. Increasing the Labour vote in the Smethwick constituency for the first time since 1950, Faulds defeated Griffiths in the 1966 general election and became Labour Member of Parliament (MP) for the constituency until his retirement in 1997. (The constituency was renamed Warley East in 1974.) Smethwick remained the focus of much racial tension in Britain throughout Faulds' time as an MP, in particular following the "Rivers of Blood" speech by Enoch Powell in 1968 which Faulds characterised as "... unchristian ... unprincipled, undemocratic and racialist." Faulds has sometimes been named as a supporter of capital punishment on the basis of off-the-cuff remarks, but he is listed in Hansard as voting against the restoration of the death penalty in 1969.
Faulds became known in the 1970s for verbally attacking Norman St John-Stevas, and said, in a heated debate over abortion, that he "has not the capacity to put a bun in anybody's oven". In 1978 he was pressured to apologise for calling John Davies, the Shadow Foreign Secretary at the time, a "fat-arsed twit"; ten years later he was scrutinised for calling David Shaw "an honourable shit".
A europhile, Faulds was one of only five Labour MPs to vote for the Third Reading of the European Communities (Amendment) Act 1993 (which gave effect in UK law to the Maastricht Treaty) in 1993. In so doing he defied his party whip, which was to abstain.