His father was a chartered surveyor and he attended a preparatory school and St. John's School, Leatherhead. He learnt to play musical instruments, studied singing and trained as an actor at RADA. He then appeared in repertory theatres, on the West End stage, At the Bristol Old Vic and on Broadway.
His earliest TV roles were as a non-speaking extra in various ITV programmes. He got his first speaking role in 1964, in the BBC's Doctor Who serial The Dalek Invasion of Earth. Smith persuaded the serial's director Richard Martin to expand the role, so that his character, Wells, appeared in three of the serial's six episodes instead of only one or two as originally scripted.
Are You Being Served? began in 1972, with Smith playing Mr. Cuthbert Rumbold, the manager of the menswear and ladieswear departments in a large fictional London store called Grace Brothers. He remained with the programme until its end in 1985, as well as appearing in the spin-off film in 1977, and the sitcom sequel Grace & Favour - known as "Are You Being Served? Again!" in the United States - in 1992 and 1993.
From September 1972, in contrast to his contemporaneous work in Are You Being Served?, he also had a semi-regular role as PC Yates in the series Z-Cars. His last appearance as Yates was in February 1975. He had a cameo in the film The Adventure of Sherlock Holmes' Smarter Brother as Sigerson Holmes' servant.
In 1978 he appeared in Worzel Gummidge as Mr Foster, the Headmaster of the school.
He appeared in the TV mini-series Martin Chuzzlewit. In 2005 Nicholas Smith was also featured in a supporting role as Vicar Clement Hedges in the Academy Award-winning film, Wallace and Gromit: The Curse of the Were-Rabbit. In 2008 he appeared as a vicar in Last of the Summer Wine.
In 2010 he appeared in children's TV programme M.I. High as Professor Quakermass.
Smith also wrote music and poetry. He is the father of actress Catherine Russell.