It would be logical to assume that people without citizenship can’t vote in the UK, same as in other jurisdictions. However, permanent residents in the UK can vote in municipal elections or Scottish parliamentary elections. In some regions of the UK, the right to vote is given to Irish and European Union citizens, e.g. in elections of the mayor of London, members of the Welsh Parliament, and members of the Northern Ireland Assembly.
At the same time, almost all local and national elections are open to nationals of countries that are members of the British Commonwealth. For example, participants of the Caribbean citizenship by investment programs can take part in an important referendum on an equal footing with the rest of the British. This is a common scenario because a Caribbean passport is often obtained as a first step to the UK residency and citizenship.