In 1970, shortly after completing his training, Lindsay debuted as Jesus in a London production of "Godspell". He alternated between TV and stage, joining the Royal Exchange Theatre Company in the late 70s, where he earned attention for playing "Hamlet" in 1983. Starring opposite Emma Thompson, he earned raves as the Cockney chap who proves to be of royal blood in "Me and My Girl". Thompson was not allowed to recreate her stage role in the USA (Maryann Plunkett inherited the part) but Lindsay was, earning numerous accolades including a Best Musical Actor Tony Award. Subsequent stage roles have included heralded portrayals of Henry II in "Becket" in 1991 and Fagin in a revival of "Oliver!" in 1996.
Before he landed his breakthrough stage role, Lindsay worked often on British TV. He was among the members of the RAF in the 1950s in the Thames TV sitcom "Get Some In!" (1975-78) before landing the role of "Citizen Smith". He perfected his Cockney accent as a pool hall denizen alongside Paul McGann in "Give Us a Break" (1983) before landing more prestigious parts like Edmund to Laurence Olivier's "King Lear" in 1984. Lindsay delivered a brilliant performance as a KGB saboteur posing as a priest in "Confessional" (Granada TV, 1990) and received a BAFTA Award as a ruthless politician in "GBH" (BBC, 1991). Lindsay also won much attention as a former SS officer being tormented by the ghost of a Jewish comedian (Antony Sher) killed in a concentration camp in "Gengis Cohn" (1993; aired in the USA on A&E).
Lindsay's film appearances have been rare. His talents were supposed to be showcased as a coal miner with showbiz aspirations in Carl Reiner's "Bert Rigby, You're a Fool" (1989), but the film did almost no box office. "Strike It Rich" (1990), an inferior remake of 1956's "Loser Takes All", teamed the actor with Molly Ringwald in a tale of a honeymooner in Monte Carlo who supposedly perfects a system for winning at roulette. More recently, he was among the zookeepers fighting for their jobs in the uneven "Fierce Creatures" and a smooth-talking businessman who revisits an old love in the comedy "Remember Me" (both 1997). Lindsay then co-starred with Julie Walters (who had played his mother in "GBH"!) as a married couple trying to change their fortunes by offering strip shows at their dingy pub in "Brazen Hussies" (lensed 1997).