The Representation of the People Act 1918 provided that only British subjects could register as electors. The term "British subject" then included any person who owed allegiance to the Crown, regardless of the Crown territory in which he or she was born. In general terms, this included citizens who became Commonwealth citizens under the British Nationality Act 1981. The then Government gave an undertaking to preserve certain existing rights of Commonwealth citizens resident in the UK, including the right to vote. This position reflects the historical ties between the UK and Commonwealth countries, rather than reciprocal arrangements.
It is not the case that every citizen of a Commonwealth country who is at any time present in the UK is eligible to be included in the register. This right is restricted in electoral law to qualifying Commonwealth citizens. They are defined as "not those who require leave to enter or remain under the Immigration Act 1971" or "those who do require leave, but for the time being have any description of such leave".