You can be registered to vote at two different addresses if you are resident at both addresses and spend an equal amount of time at each.
For example, students can be registered at their home and term time addresses. The final decision as to who is eligible to register at an address rests with the electoral registration officer for that area.
It is an offence to vote twice in the same election, such as at a general election. However, you can vote in elections at two separate local councils.