Jeffries attended the Queen Elizabeth Grammar School, Wimborne Minster, Dorset. In 1945, he received a commission in the Oxford and Buckinghamshire Light Infantry. After his World War II service, for which he was awarded the Burma Star, he trained at RADA. He entered repertory at the David Garrick Theatre, Lichfield, Staffordshire for two years and appeared in early British television plays. Jeffries built a successful career in British films mainly in comic character roles and as he was prematurely bald he often played characters older than himself, such as the role of father to Caractacus Potts (played by Dick Van Dyke) in the film Chitty Chitty Bang Bang (1968), although Jeffries was actually six months younger than Van Dyke. His acting career reached a peak in the 1960s with leading roles in other films like Two-Way Stretch (1960), The Trials of Oscar Wilde (1960), First Men in the Moon (1964) and Camelot (1967). Jeffries turned to writing and directing children’s films, including a well regarded version of The Railway Children (1970) and The Amazing Mr Blunden (1972). He was a member of the British Catholic Stage Guild.

Jeffries had a dislike of television and its production values and shunned the medium for many years. He reluctantly appeared on television in an acting role in the 1980 London Weekend Television Dennis Potter drama Cream in My Coffee and realised that television production values were little different from those in the film industry; as a result he launched a belated career in television. He appeared in an episode of the Thames Television/ITV comedy-drama Minder in 1983, played a leading role in the situation comedy Roll Over Beethoven (Central Television/ITV) and appeared in an episode of Inspector Morse in 1990 (Central Television/Zenith/ITV). During location filming for an episode of the 1983 Thames/ITV situation comedy Tom, Dick and Harriet, Jeffries and his co-stars Ian Ogilvy and Bridget Forsyth had to be rescued when a stunt involving a car went wrong. Jeffries retired from acting in 2001 and his health declined in the following years. He died on 19 February 2010 in a nursing home in Poole, Dorset. He had suffered from vascular dementia for the last twelve years of his life. He had been married to Eileen Mary Walsh from 1951 until his death. Their son and two daughters also survived him. Jeffries’ granddaughter is the novelist and playwright Amy Mason.