There is a little bit here about why:
http://en.wikipedia.org/wiki/The_Curse_of_Step toe
When they wrote Steptoe and son the writers wanted actors rather than comedians playing the 2 main parts.
Harry H Corbett (the son) was a promising actor at the time who probably saw the chance to act in a TV comedy (with serious overtones) as a good career move.
But the show was so sucessful that he was typecast in the role for the rest of his life and found it hard to get any other work.
The show did finish in 1965 but came back again in 1970 when Harry realised that was almost the only work he could get.
In a funny sort of way, the frustration he felt in the show was mirrored in real life as he felt his "father" was holding him back as a serious actor and this led to friction.
Brambell was also homesexual which at the time was a no-no and that also probably caused friction between them.