Peacock's many television roles include Jim Trott in The Vicar of Dibley, Rouault in Madame Bovary (opposite Keith Barron), Quilp in The Old Curiosity Shop and Old Bailey in Neverwhere.

He appeared in a wide variety of programmes, such as EastEnders (playing Sid, a war veteran Alfie Moon met in France), LWT's Wish Me Luck (in which he played resistance leader Renard), Jonathan Creek, Between the Lines, The Riff Raff Element, The Thin Blue Line, My Family, and in a 1990 episode of Van der Valk.

Peacock had starring roles in several plays in the BBC Television Shakespeare series, including the title role in Titus Andronicus, Feste in Twelfth Night, Lord Talbot in Henry VI, Part 1 and Jack Cade in Henry VI, Part 2.

Peacock appeared as "Captain Zero" in the BBC TV series Last of The Summer Wine (1990) and as Maurey in The Sins (2000).

[7] Other hit songs to his credit include "Mystery Girl" (recorded by Jess Conrad),[8] "Made You" (Adam Faith),[9] "Gossip Calypso" (Bernard Cribbins),[10] "Stick Around" (Billy Fury),[11] "That's What Love Will Do"[12] and "Nature's Time For Love"[13] (both recorded by Joe Brown).

[15] In 2002 he filmed an episode of Dinotopia in Budapest, playing the mysterious sage Lok in "Night of the Wartosa".

These include: In the 1970s he became a member of the Royal Shakespeare Company, playing comic roles such as Silence and Feste, as well as more serious parts.

[21] Peacock was diagnosed with dementia in 2009, and it was reported in 2018 that he was in the advanced stages of the disease, had retired from acting and was living in a nursing home in Yeovil, Somerset.