I know in the Glamorgan Record Office the electoral registers are one of the most popular of resources searcher view (behind parish registers, of course). The GRO only holds those for Glamorgan naturally, but I can only presume that in other counties they also hold that areas registers in their county archives. In some cases local libraries (where there's a reference library) also hold copies of the registers for the electoral constituency they are in.
Electoral registers, however, don't give nearly half as much information as people expect. The vast majority of researchers who come in or write to Glamorgan at least seem to be of the view that the registers exist as a form of replacement for the census. That isn't the case. Of course, they only record those people who were registered to vote...and pretty much all the information you get is address, name, and qualification to vote.
In theory they should go back to at least 1832 when, if I remember correctly voting registration was introduced as part of the Reform Act...but it's very much dependent on area, and there are gaps. There may be earlier registers depending on the area and no doubt depending on what qualification to vote they were using in an individual borough. There are also no registers for the war years.