Hoskins was born in Bury St Edmunds, Suffolk, England, the son of Elsie Lillian (née Hopkins), a cook and nursery-school teacher, and Robert William Hoskins, Sr., a bookkeeper and lorry driver. One of Hoskins' grandmothers was a Romani. In 1967, while aged 25, he spent a short period in kibbutz Zikim in Israel.

According to the production notes on the Special Edition of Who Framed Roger Rabbit, his acting career started when he was sitting in a pub enjoying a beer. When someone came up to him, told him to go upstairs to audition for a play, so he did and actually got the role. Before that day a career in acting was the last thing he ever thought he'd have.

After beginning his acting career on the London stage in the late 1960s, Hoskins first gained wide attention in the original BBC television serial version of Dennis Potter's Pennies from Heaven as sheet music salesman Arthur Parker and On the Move (both 1978), an educational series intended to tackle adult illiteracy. Later, he played Iago in Jonathan Miller's BBC Television Shakespeare production of Othello.

Hoskins' performances in British films such as The Long Good Friday (1980) and Mona Lisa (1986) won him the wider approval of the critics and, in the case of the latter, a Cannes Award, Best Actor Golden Globe and BAFTA Awards and an Academy Award nomination for Best Actor.

He also delivered comic turns in Terry Gilliam's Brazil (1985) and Super Mario Bros. (1993). Hoskins was not initially aware that Super Mario Bros. was based on the popular video game of the same name. His son had asked him what film he was working on, and recognizing it, showed Hoskins the video game on the Nintendo video game console.

In a 2007 interview, he revealed that he was not happy with the film or his experiences making it, referring to it as the "worst thing I ever did". During the late 1980s and early 1990s he appeared in advertising for the recently privatised companies of British Gas and British Telecom (now BT Group).

Hoskins made a cameo appearance as a rock band's manager in the Pink Floyd film The Wall, with a two-word expletive spoken part. He has also directed films. He was slated to be a last-minute replacement in the film The Untouchables if star Robert De Niro had not decided to play Al Capone.

When De Niro took the part, director Brian De Palma mailed Hoskins a cheque for US$ 200,000 with a Thank You note, which prompted Hoskins to call up De Palma and ask him if there were any more movies he didn't want him to be in.

Hoskins' first appearance to mainstream American audiences was in Who Framed Roger Rabbit, for which he received a second Golden Globe nomination. Some of Hoskins' other notable appearances include playing opposite Cher in Mermaids (1990), boatswain Smee to Captain Hook in Hook (1991), and Uncle Bart, the violent "owner" of Jet Li in Unleashed.

He has also performed in several television productions for the BBC, including Dennis Potter's Pennies From Heaven, Flickers, David Copperfield, and Wind in the Willows. He played Nikita Khrushchev in the movie Enemy at the Gates (2001). Khrushchev was shown in his political commissar days during the Battle of Stalingrad. He received a Golden Globe nomination for Best Supporting Actor for his performance in Mrs Henderson Presents.