He was born Peter Ewart Ohm on 4 April 1923, in Wem, Shropshire, the son of a bank clerk, Max Ohm, who was an Austrian immigrant, and Eva Wright, a nurse. The family later moved to Wellington in the same county, where he began schooling; he later said it was while reciting a poem at infant school in Wellington that he experienced the applause and admiration coming from a good performance. He was brought up from the age of seven in Staffordshire where he attended Uttoxeter Grammar School.

After leaving school he joined Wolverhampton Repertory theatre and gained experience in other repertory theatres before army Service in the Second World War. He was commissioned a second lieutenant in the Royal Corps of Signals on 9 June 1943, and served in Normandy, Belgium and the Far East. At the end of the war, he was in Singapore and present during the liberation of Changi Prison.

The first of Vaughan's two marriages was to Billie Whitelaw, whom he married in 1952 and divorced in 1966. His second wife was Actress Lillias Walker, with whom he lived in the village of Mannings Heath, in West Sussex until his death, having previously lived in Crawley. His stepdaughter Victoria Burton (actress and producer) is married to Gregor Fisher.

In film, he made his debut in 1959 in an uncredited role as a police officer in The 39 Steps. He continued for several years to play small parts, including more cameos as policemen in Village of the Damned and The Victors before gaining his first starring role, in a minor picture called Smokescreen (1964), where he played an insurance assessor investigating a businessman’s disappearance in one of the last, and best, of the old-style British B-movies. In 1967, he received second billing opposite Frank Sinatra in the film The Naked Runner. However, his performance was not well received by critics who accused him of overacting in his role as a British agent. He played Mr. Freeman in Karel Reisz's 1980 The French Lieutenant's Woman, alongside Meryl Streep and Jeremy Irons.

Vaughan's first breakout role was in 1964 as Ed in Joe Orton's work Entertaining Mr Sloane performed at Wyndham's Theatre.

In 1969, he appeared in Randall and Hopkirk in the episode "Never Trust a Ghost". The same year he starred in the thirteen-part LWT TV series The Gold Robbers. In December 1972, he appeared as Mr. Paxton in the BBC television adaptation of the M.R. James ghost story A Warning to the Curious, shown as part of their annual series A Ghost Story for Christmas.

He became known for his performances on television, including supporting roles in Porridge (as "Genial" Harry Grout) and Citizen Smith as Charles Johnson, (although his role in the latter series was taken over by Tony Steedman). Vaughan's role in Porridge brought him a great deal of public recognition, despite the fact that his character appeared in only three episodes and the 1979 film of the series.

Vaughan starred as Billy Fox in the Thames Television series Fox (1980). The saga was written by Trevor Preston, directed by Jim Godard, and produced by Verity Lambert. As other Fox family members it also starred Elizabeth Spriggs, Ray Winstone, Larry Lamb and Bernard Hill. Historical roles Vaughan played include the role of Russian ambassador Alexander Izvolsky in the serial Fall of Eagles (1974), British Politician Thomas Inskip in the mini-series Winston Churchill: The Wilderness Years (1981), the title role in A Last Visitor for Mr. Hugh Peter (1981), and German Nazi figures Kurt Zeitzler in the miniseries War and Remembrance (1988) and Hermann Göring in the docu-drama Countdown to War (1989). He also appeared in many literary adaptations, such as Bleak House (BBC, 1985), in which he played the sinister Lawyer, Mr Tulkinghorn and Our Mutual Friend (BBC Two, 1998). Other television work includes the espionage thriller Codename: Kyril (1988), in a lead role as the head of the KGB.

Vaughan was heard as Superintendent Kirk in the BBC dramatisation of Dorothy L. Sayers' Peter Wimsey novel Busman's Honeymoon, and as Denethor in the 1981 BBC Radio production of The Lord of the Rings.

In 1986, he appeared in the promotional video for Kate Bush's "Experiment IV" single. In 1991, he played John Turner in an episode of the Granada Television's The Adventures of Sherlock Holmes titled 'The Boscombe Valley Mystery', with a convincing Australian accent.

Possibly his highest-profile film performance was as the father of Anthony Hopkins' character in The Remains of the Day (1993). He was also cast in Terry Gilliam's The Man Who Killed Don Quixote, but had not shot any material before that project was abandoned. He had previously appeared for Gilliam in Time Bandits and Brazil. He also appeared as a menacing character in Straw Dogs (1971), and with Bill Murray in a film of W. Somerset Maugham's novel The Razor's Edge in 1984. In 1996, he appeared as Giles Corey in The Crucible, and in 1997 he appeared alongside Robert Carlyle and Ray Winstone in Face. In 1998, he appeared as Bishop Myriel in Les Misérables alongside Liam Neeson. His most unusual role may have been as SS Obergruppenführer Arthur Nebe in the 1994 film of Robert Harris's novel Fatherland.

Vaughan later attained particular acclaim for his supporting role as the eventual Alzheimer's sufferer Felix Hutchinson across thirty years of his life in Our Friends in the North (BBC Two, 1996), a role which gained him a Best Actor nomination at the 1997 British Academy Television Awards.

In 2007, he starred in the television serial Mobile and as Uncle Alfie in the film Death at a Funeral. In 2011, Vaughan starred as Michael Dodd in the BBC courtroom drama Silk. His final role between 2011 and 2015 was Maester Aemon in the HBO series Game of Thrones.

Vaughan was partially blind. He died peacefully at 10:30 AM (GMT) on 6 December 2016 at the age of 93 from natural causes.