EU nationals citizens legally resident in the UK may currently register to vote in all elections that use the local government franchise. However, the Government has recently proposed changes to legislation as a result of the UK’s exit from the EU. Provisions included in the Elections Bill 2021-22 would restrict voting rights for EU citizens living in England and Northern Ireland who entered the UK after the end of the Implementation Period, 31 December 2020, to those from countries where a bilateral agreement has been agreed between the UK and individual member states. So far this covers Spain, Portugal, Poland and Luxembourg and only citizens for those 4 EU countries will keep their voting rights in local elections in England and NI. EU citizens who were living in the UK prior to the end of the Implementation Period will maintain their local voting and candidacy rights in England and Northern Ireland, provided they retain lawful immigration status. The voting restriction does not apply to EU citizens living in Scotland and Wales. They will retain their existing voting rights as all legally resident foreign nationals can register to vote for local and devolved elections.
I've updated the title with a question mark as I've got doubt that it will pass the parliament procedure before the next election in May. The bill is only with the Lords currently and they will certainly amend it.