Gilmore starred in 91 episodes of the BBC series, from 1971-1981, which followed the lives of shipping magnate James Onedin and his family.
Co-star, actress Jessica Benton, called him “a gentle man and a gentleman”.
She 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.
“We sorely miss him.”
In 1958 he got his first major part as Sir Waldo of Ivanhoe in the TV series, Ivanhoe, before West End roles.
In 1971, Gilmore was cast as the shrewd and determined shipping boss James Onedin in the BBC’s ambitious drama series.
Other roles included Casualty and Heartbeat, his final on-screen role was in a made-for-TV film, On Dangerous Ground, with Rob Lowe.