- He had been a professional actor for twenty years before starting to work in films, but was then in so many over the next 25 years that the film critic Barry Took remarked that, if he ever saw a British film that Andrews wasn't in, he began to worry, "because I realize he must have been ill".
- He was badly injured when riding a horse while making a film in 1972. It caused him various health problems for the rest of his life.
- He served with the Royal Artillery, 1939 -1945, during World War II. ending up as acting major. At the end of the war he took some of his men to see Laurence Olivier at the Old Vic. Olivier recognised him as before the war Harry had been Tybalt to Olivier's Romeo and within weeks Harry was back on stage as a member of the Old Vic company.
- He was awarded the CBE (Commander of the Order of the British Empire) in the 1966 Queen's Birthday Honours List for his services to drama.
- Attended Wrekin College in Shropshire, England.
- After his death, one obituary noted that "his death has given casting directors all over the world an insoluble problem".
- Longtime companion of Basil Hoskins.
- He appeared in four films directed by Sidney Lumet: The Hill (1965), The Deadly Affair (1967), The Sea Gull (1968) and Equus (1977). Andrews sometimes said that Lumet was his favorite director, whilst Lumet called him one of Europe's finest actors.
- Appeared in seven films with Michael Hordern: Alexander the Great (1956), I Accuse! (1958), I'll Never Forget What's'isname (1967), The MacKintosh Man (1973), Theatre of Blood (1973), Đồi Thỏ (1978) and The Medusa Touch (1978).
- In his spare time he enjoyed playing cricket.
- He was cast as Major Swindon in "The Devil's Disciple" at the absolute insistence of Laurence Olivier, who wouldn't do the film without him. Andrews never forgot this.
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