You can't.
Well, slight exaggeration. There are a couple of websites with results for very specific areas; David Boothroyd has published ward results for Westminster and Paddington since 1900 and Tower Hamlets 1964-1998, a former LibDem councillor in Sheffield has published results going back a couple of decades. There's probably more out there that I don't know about. Also, there's some stuff on wikipedia; Manchester has especially good coverage (goes back to the mid 1970s, IIRC). Newcastle used to have an archive going back to 1982 on their website, but it was scrapped years ago.
I once stumbled across a ridiculously far back local election results archive for Harrow, but I'm damned if I can find it now. I remember seeing something similar for Wigan (or was it Barnsley?).
For results from about 1995 onwards you could always give archive.org a go.
