There is a sort of antiques and collectibles fair every month where I live and there are two or three stalls which have old maps (1920s to 1950s).
Two main types of map to look for:
The old Ordnance Survey 'one-inch' maps (like the modern Landranger series). Exactly the same as modern, except scale is 1:63360 instead of 1:50000 (so slightly smaller but mapping looks very similar)
Bartholomew's "county" series (now discontinued): these have coloured contours (like a schoolbook atlas) and the scale was half-inch to the mile. As their title suggested, they mainly covered a single county each (though depends on the type of the county!) Very popular with walkers and cyclists.
If you have boot- or other fairs in your area, try these.
Charity shops often have a few of these old maps in among the books.
I wouldn't recommend old road maps because they tend to show roads but not much else. (Though some are better than others.)