Hancock was the first of a line of humorous but whingeing British males, a tradition that continues into the present. The Hancock persona is recognisable in, for example, Richard in 'One Foot in the Grave' and Basil in 'Fawlty Towers'.
It is a style of humour strictly for British and Commonwealth audiences. It does not export to the US although the US has tried to copy the genre, not particularly consistently or well (q.v. Archie Bunker).
By the time Hancock made the television series he had fallen out with the stalwarts of the radio show, Sid James, Kenneth Williams, and Hattie Jacques. He felt they were more loved by the audience than he was -- and perhaps the audience was right. They were missed and the TV series suffers from their absence. Hugh Lloyd and Patrick Cargill, although well-known light comedy actors, just weren't of the same calibre or popularity. Hattie Jacques was irreplaceable.
However, the scripts of Ray Galton and Alan Simpson and Hancock's own undoubted talent almost save the day. The episode 'The Blood Donor' is still rated one of the top 10 comedy sketches of the century (in Britain) and deservedly so.
After the TV series Hancock's star waned rapidly -- he should have stuck to Sid James and crew -- but he was too much the egotistical star. He toured Australia and was booed off the stage -- staggeringly drunk -- at the Dendy Theatre, Brighton (Melbourne), Vic. The following week he suicided in his hotel room in Sydney (must be something about Sydney!)