Callow's immersion in the theatre began after he wrote a fan letter to Sir Laurence Olivier, the artistic director of the National Theatre, and received a response suggesting he join their box-office staff. While watching actors rehearse, he realised he wanted to act.
Callow made his stage debut in 1973, appearing in The Three Estates at the Assembly Rooms Theatre, Edinburgh. In the early 1970s, he joined the Gay Sweatshop theatre company and performed in Martin Sherman's critically acclaimed Passing By.[6][7] In 1977, he took various parts in the Joint Stock Theatre Company's production of Epsom Downs, and in 1979, he starred in Snoo Wilson's The Soul of the White Ant at the Soho Poly.
Callow appeared as Verlaine in Total Eclipse (1982), Lord Foppington in The Relapse (1983), and the title role in Faust (1988) at the Lyric Hammersmith, where he also directed The Infernal Machine (with Maggie Smith) in 1986. In 1985, he played Molina in The Kiss of the Spiderwoman at the Bush Theatre, London. He played Mozart in the premiere of Peter Shaffer's Amadeus at the National Theatre (1979), also appearing in the 1983 BBC original cast radio production.
He later wrote of having "discovered Mozart quite early: the operas, the symphonies, the concertos, the wind serenades were all very much part of my musical landscape when I was asked to play the part of the composer in Peter Shaffer's Amadeus; possibly this was one of the reasons I got the job." He also appeared at the National Theatre as Orlando in As You Like It (1979) and Fulganzio in Galileo (1980).
He made his first film appearance in 1984 as Schikaneder in Amadeus. The following year, he appeared as the Reverend Mr. Beebe in A Room with a View. His first television role was in the Carry On Laughing episode "Orgy and Bess" in 1975, but it was cut from the final print. He starred in several series of the Channel 4 situation comedy Chance in a Million, as Tom Chance, an eccentric individual to whom coincidences happened regularly. Roles like this and his part in Four Weddings and a Funeral brought him to a wider audience.