The show is actually more or less a continuation of the characters from
Ray Galton and
Alan Simpson's previous hit TV/radio series
Hancock's Half Hour (later retitled
Hancock).
While the names of the characters and their relationships have changed, there is a striking resemblance between the character of Albert Steptoe and that of Sid (as played by Sid James in the Hancock shows) - both are devious, physically unclean, resolutely working class and always looking for a way to make money for themselves. Harold Steptoe on the other hand bears a striking resemblance to Tony Hancock's character - embarrassed by his father/flatmate, with pretentions 'above his station' of intelligence, status and sophistication.
Galton and Simpson have both said that the series is how they saw Hancock ending up, but Tony Hancock resolutely refused to have his character degraded beyond a certain extent, and stopped working with the writers.
While the characters are obvious variations on well established comic archetypes (Laurel and Hardy, Lister and Rimmer from Red Dwarf, Pete & Dud are just three examples) the emphasis on class mobility is unique to Britain, and to the 60s - the first time in British history when it seemed possible for working class people to achieve 'above their station'.
BTW for US people who don't know the show, Wilfred Brambell (Albert Steptoe) played Paul McCartney's grandfather in A Hard Day's Night. A further little trivia note - he was originally slated to play the bass player in Frank Zappa's 200 Motels until Ringo Starr's chauffeur, Martin Lickert, stepped in!