Guyler was born in Wallasey on the Wirral Peninsula, Cheshire, and brought up on the other side of the River Mersey in Liverpool, Lancashire, where his father was a jeweller. He attended Liverpool College and originally planned a career in the church. In the 1930s he joined the Liverpool Repertory Theatre and performed in numerous productions. During the Second World War he was called up and joined the RAF Police but was later invalided from service, whereupon he joined Entertainments National Service Association (ENSA) and then (on 4 May 1942) the BBC's Drama and Repertory company in Manchester.
During the war, he became a regular on the immensely popular radio series, It's That Man Again (ITMA), a series built around comedian Tommy Handley. Guyler claimed that his character 'Frisby Dike' (named after a Liverpool department store bombed in the Blitz) was the first time the real Liverpudlian accent was heard on the radio. He took part in a Royal Command Performance of ITMA for King George VI and Queen Elizabeth in December 1947. Guyler remained with the show until the death of Handley in 1949 when the series ended.
After ITMA, Guyler worked in varied roles from BBC Children's Hour to classical parts, including with John Gielgud in King Lear. He was known for his often amusing asides in rehearsals. For a Children's Hour documentary about life in the coal mines, which Guyler was narrating, the producer had visited a mine and recorded most-realistic sound effects. As these were banging, crashing and thumping sounds he was heard to mutter: "Sounds like a Peter Brook production".
In the 1950s, he played the time-traveller (also known as "the voice") in the British sci-fi radio series Journey Into Space. Guyler then took on the role in the title character of a Scotland Yard detective in the Light Programme series Inspector Scott Investigates, created by John P. Wynn, that ran from 1957 to 1963. During the half hour programme a crime was committed; Scott and his sidekick, Det. Sgt. Bingham (Brian Hayes, brother of Patricia Hayes) interviewed two or three suspects; then, while music played, there was a short intermission for listeners to guess 'whodunit' before the final reveal. In Henry Reed's series of radio dramas about Herbert Reeve's inquiries into the life of Richard Shewin, Guyler played General Gland, soldier-scholar, campanologist and author of war memoirs, most notably in Not a Drum was Heard. During the 1960s and 1970s, when he starred in the satirical radio programme about life in the British civil service The Men from the Ministry with Richard Murdoch, Guyler played the pompous, self-important Number One in the General Assistance Department, with Murdoch as his diffident but equally incompetent Number Two.