The star, who grew up in North Yorkshire, died at the Trinity Hospice in London after a “long illness”, his family said.
Gilmore also appeared in a number of Carry On films as well as numerous TV dramas such as Doctor Who, The Persuaders, Ruth Rendell Mysteries and Heartbeat.
But he will be best remembered for his portrayal of the mutton-chopped lead, James Onedin, in 91 episodes of BBC1 series The Onedin Line.
The saga – with its theme tune familiar to a generation – followed the fortunes of a family shipping line in the second half of the 19th century.
His co-star Jessica Benton, who also appeared in other BBC period dramas The Duchess Of Duke Street and Upstairs, Downstairs, said: “The Onedin Line was a very happy, long-running series to be involved in and that was all credit to Peter because he made it so.
“We all became very close friends over the years and had a lot of fun. Peter was a gentle man and a gentleman and we sorely miss him.”
Born in Leipzig, Germany, he came to the UK at six and was raised in Nunthorpe, leaving school at 14 to pursue an acting career.
His big break was in the TV series Ivanhoe in 1958, and he went on to appear in West End musical stage successes such as Lock Up Your Daughters and The Beggar’s Opera.
Among his many films, he appeared in popular comedies such as Carry On Up The Khyber and Carry On Henry and the ghoulish British horror film The Abominable Doctor Phibes.
Gilmore – who died on Sunday – was married to actress Una Stubbs for more than a decade and went on to marry Anne Stallybrass, who also played his wife in The Onedin Line.
His agent Primie Carey, of Roger Carey Associates, said: “On behalf of his wife Anne and Peter’s family I would like to thank those who have sent their kind thoughts and condolences.”