The printed electoral rolls have always been, and remain, public documents. (It's only the modern electronic versions, in their unedited form, that aren't open to the general public). So you can walk into any relevant council office and demand to see the current unedited roll for the area in printed form. It's your legal right. (I've done it lots of times).
Since the electoral roll for a specific period was in the public domain at the time of its publication, there are no laws protecting the information at a later date. However many librarians and archivists seem to misunderstand the Data Protection Act and impose unnecessary restrictions upon access to the data. That leads to lots of discrepancies between the policies of different organisations.
For example, in the days before '192.com', the then current national electoral roll was available on CD and available in most public libraries. I frequently used those CDs in Ipswich library, and in other libraries in East Anglia. However when I asked for the CD in a London library I was told (in very strong terms) that
(a) I would be breaking the Data Protection Act if I was to ever consult one of those CDs ; and
(b) the library would be breaking the Data Protection Act by simply having such a CD on its premises, even if they didn't make it available to anyone!
That librarian was, of course, talking utter rubbish but it illustrates the level of misinformation that is fed to people whose job it is to supply accurate information!
Further, as well as seeking to conform with the Data Protection Act, each local studies centre will have its own policy as to how long documents referring to named individuals must be protected (and also their own rules as to which documents fall within that policy). For example many local studies units will make the log books of old schools available immediately they come into their possession but information relating to named teachers or children (such as school punishment books) is kept private for, typically, 80 or 100 years.
So once again there will be differences between centres. Some will regard certain information as coming within (say) an '80 year rule', while others won't and yet others might not even have such a rule.