Trevor will be best remembered for his portrayal of farmer Jim Trott in the hit British comedy, a role he played in all three seasons of the show and its numerous one-off specials.
The news of his death was announced by his agent on Tuesday morning.
Remembering him as an “actor, writer and songwriter”, a statement on behalf of his family revealed that Trevor had died on Monday morning “from a dementia-related illness”.
Following the announcement, Dawn French paid tribute on Twitter, sharing a behind-the-scenes photo of herself and Trevor.
She wrote: “Night Trev. I love you.”
As well as playing Jim in The Vicar Of Dibley, Trevor had numerous TV and theatre credits to his name.
These included the TV drama Family Business, the festive comedy film Fred Claus and a 2005 appearance in EastEnders.
In the 1960s, he also appeared alongside The Beatles in a TV special, as well as numerous roles in the BBC Shakespeare series in the late 70s and early 80s.
Trevor made his final on-screen appearance in 2015, playing Jim in a Comic Relief special of The Vicar Of Dibley.
In addition to his acting career, Trevor was a songwriter, penning hits for Herman’s Herbits, Joe Brown and The Vernons Girls.
He also penned the lyrics for a musical adaptation of the comic strip Andy Capp, along with The Animals musician Alan Price.
Trevor was first diagnosed with dementia in 2009, and in 2017, it was reported that he had retired from acting as a result of his condition, and was living in a nursing home.
He is survived by his four children Daniel, Harry, Sally and Maudie.