Hollywood stars including Samuel L. Jackson and James Woods led tributes from the world of film, while his family spoke of their grief.
"We are devastated by the loss of our beloved Bob," said a statement from his wife Linda and the couple's two children Rosa and Jack, as well as Hoskins's two children from his first marriage, Alex and Sarah.
"Bob died peacefully at hospital last night surrounded by family, following a bout of pneumonia," they said.
Hoskin's face was carried on the front page of Thursday's Independent newspaper and the Daily Telegraph's headline paid tribute to a "great actor and even greater man".
The Guardian called Hoskins "a man for the big role", the Daily Mail a "pint-sized street fighter with a giant talent", while the Sun signed off its editorial page by saying "RIP Bob, you were a one-off."
- Circus job -
Born in Suffolk in eastern England after his mother was evacuated from London during World War II, Hoskins left school at the age of 15 and worked in a series of odd jobs, including in a circus and as a lorry driver.
He claimed he only got into acting by accident, after being mistakenly called to try out for a play while waiting for a friend to finish his audition.
Hoskins began working in TV and broke through into film with his portrayal of a doomed London gangster in "The Long Good Friday" in 1980, which won him a Bafta nomination.
Despite his diminutive stature, he was a powerful presence on screen, exuding seething, barely-concealed anger.
But he also had a comic touch, and one of his best known roles was as the detective trying to work out "Who Framed Roger Rabbit?", the eponymous cartoon hero, for which he was nominated for a Golden Globe in 1989.
Although Hoskins was known for his distinctive Cockney accent, he renounced it for an American drawl when the work required, including in "Nixon", in which Hoskins played former FBI chief J. Edgar Hoover.
He claimed he was on standby to play Al Capone in Brian De Palma's Oscar-winning 1987 thriller "The Untouchables" before Robert De Niro agreed to the role.
More recent success came with a Globe nomination in 2006 for "Mrs Henderson Presents" with Judi Dench, while other hits included his role as the sailor Smee in Steven Spielberg's "Hook" and "Mermaids" with Cher and Winona Ryder.
Dench told BBC News she was "so very sorry to hear this news."
Fellow dame Helen Mirren said Hoskins had been "supportive and unegotistic" when they worked together on The Long Good Friday.
"I had the honour of watching the creation of one of the most memorable characters of British film," she added.
- 'A gentleman' -
Hoskins was highly prolific and many of his films sank without a trace, a fact some critics attributed to his claim never to prepare for a new job.
But there was an outpouring of affection on Twitter following news of his death.
Samuel L. Jackson was one of the first to pay tribute, saying he was "truly saddened" at his death. "A truly gigantic talent & a gentleman. R.I.P," the film star said on Twitter.
James Woods, who starred with Hoskins in Oliver Stone's biopic "Nixon" in 1995, tweeted: "Oh man, what a terrible loss. A great guy and a superb artist."
Hoskins' last acting role was as one of the seven dwarves in the film "Snow White and the Huntsman", starring "Twilight" actress Kristen Stewart.