What few people know is:

If you work between April and your move, you will pay income tax on each pay period as if you are going to see out the full year. The great news is if you are moving permanently you will be owed money in back taxes as your UK tax free allowance will be a greater percentage of your earnings compared to a full 12 month period.

Depending on your experience with HMRC you can claim online, through self-assessment or through a postal form.

I gave a close relatives postal address to my former employer and HMRC for all mail post service.

Your P45 can take a while to arrive in the mail or on HMRC online, but once it does you can claim a refund via form P85