Bad Penny Blues" in 1956, a single produced by Joe Meek. It was on the charts for 6 weeks. It wasn't a career, but it got him on the BBC where he began doing big band broadcasts. [Side note: he became more versatile as a trumpeter and moved onto bebop, rock and even once recorded with Radiohead.]
In 1967 he began hosting his own jazz program,The Best of Jazz on BBC Radio 2. The program is everything you'd expect of jazz on the BBC in the 1960s, stiff delivery and a varied playlist. Btu that show didn't make his career either. It was another strange break 5 years later which took his deadpan delivery and put him in the position of host wrangling a cast of hyperactive comedians through a chaotic panel program. That comedy show was the British radio
comedy institution "I'm Sorry I Haven't A Clue" (ISIHAC). I believe it was because of it's iconic success, that his jazz
program lasted for 40 years.
The BBC describes ISIHAC as "The long-running, self-styled antidote to panel games." I use the word institution because it was on from 1972 until his death in 2009 — a run of 37 years. The BBC rebooted the show in 2009 with Lyttelton being replaced by a three rotating hosts: Stephen Fry, Jack Dee and Rob Brydo. We all know Stephen Fry but I don't know the other two blokes at all. Ultimately jack Dee inherited the podium.
The show actually spring form another show called "I'm Sorry, I'll Read That Again" which was a familiar looking sketch comedy program among whose writers was John Cleese. The BBC had already broken ground on quiz shows with no competition or winner. The show was voted the second funniest radio program ever; beaten out only by The Goon Show. More here.