Ron has worked in a variety of genres, but is perhaps best known for his starring role as Fagin in Lionel Bart's stage and film musical Oliver! based on Oliver Twist by Charles Dickens. He created the role in the original West End production, and reprised it in 1984 on Broadway and in the 1968 film, for which he was nominated for the Academy Award for Best Actor and won the Golden Globe Award for Best Actor - Motion Picture Musical or Comedy.
He appeared in several children's television series, including The Animals of Farthing Wood, Noah's Island, Telebugs, Into the Labyrinth, and the Discworld series. Among his better known roles is that of Prime Minister Rupert Mountjoy in the comedy The Mouse on the Moon (1963), alongside Margaret Rutherford. He played French entertainer and mime artist The Great Orlando in the 1963 Cliff Richard film Summer Holiday. He acted again with former Oliver! co-star Jack Wild in Flight of the Doves.
In 1969, Moody was offered, but declined, the lead role in Doctor Who, following the departure of Patrick Troughton from the part. He later told many people (including Doctor Who companion Elisabeth Sladen) that declining the role was a decision he subsequently regretted. He played Edwin Caldecott, an old nemesis of Jim Branning in EastEnders. He played Ippolit Vorobyaninov alongside Frank Langella (as Ostap Bender) in Mel Brooks' version of The Twelve Chairs (1970). In 2003, he starred in the black comedy Paradise Grove alongside Rula Lenska. In 2005, he acted in the Big Finish Productions Doctor Who audio play Other Lives, playing the Duke of Wellington.
In 2004, the British ITV1 nostalgia series After They Were Famous hosted a documentary of the surviving cast of the motion picture Oliver!. Several of the film's musical numbers were reenacted. Moody, then 80 but still spry, and Jack Wild (seriously ill with oral cancer at the time) recreated their dance from the closing credits of the film.
Moody appeared in an episode of BBC1's Casualty (aired on 30 January, 2010) as a Scottish patient who had served with the Black Watch during the Second World War.
On 30 June 2010, Moody appeared on stage at the end of a performance of Cameron Mackintosh's revival of Oliver! and made a humorous speech about the show's 50th anniversary. He then reprised the "Pick a Pocket or Two" number with the cast.