He co-starred with Boris Karloff in The Sorcerers, with James Mason, Bobby Darin, and Geraldine Chaplin in Stranger in the House (1967), with Vincent Price in Witchfinder General, with Tom Courtenay and Candice Bergen in The Day the Fish Came Out, with Meryl Streep and Goldie Hawn in Death Becomes Her, with Peter Cushing in two films for horror specialists Amicus and with Richard Dreyfuss and Nia Vardalos in My Life in Ruins – among others.

Ogilvy was married to Diane Hart from 1968–83; they had one child. He married Kathryn Holcomb in 1992, and later became a naturalised United States citizen.

Ogilvy has had an extensive career in the theatre playing leading roles in many London West End productions, including Design for Living, Happy Family, Three Sisters, Rookery Nook by Ben Travers, Run for Your Wife, The Millionairess by Shaw, The Waltz of the Toreadors, and others. He has also worked widely in the American theatre. Among his films, Ogilvy had a major part in the 1970 epic film Waterloo.

In 1976, he featured in the pilot episode of the television comedy series Ripping Yarns, co-produced by former Monty Python members Michael Palin and Terry Jones. He also appeared in I, Claudius (as Drusus), and guest-starred in 6 episodes of Murder, She Wrote and 4 episodes of Diagnosis Murder. He appeared as Edgar Linton in the 1970 film version of Wuthering Heights and as Owen Gereth in 1970's BBC dramatisation of The Spoils of Poynton.

He is best known as the star of the television series Return of the Saint (1978–79), in which he assumed the role of Simon Templar from Roger Moore (1962–69).

He was the subject of This Is Your Life in 1979 when he was surprised by Eamonn Andrews.

He recorded a series of readings of Ian Fleming's James Bond novels in the early 1980s, which were released on audio cassette by the Listen for Pleasure label.

In the 1990s, he guest-starred in the American television series Babylon 5, in the 1998 episode "In the Kingdom of the Blind". The series' star, Bruce Boxleitner, is the former husband of Ogilvy's second wife, Actress Kathryn Holcomb.

He has written and published two novels – Loose Chippings and The Polkerton Giant – and two plays: A Slight Hangover and Swap!, currently running in Poland in its third successful year. His memoir, Once A Saint, was published by Little Brown/Constable, in May 2016.