Right, I changed schools at the end of year 12 due to school closure so didn't have much choice. The only major problem I run into was matching up exam boards, as you will need permission from the exam board you're changing to and won't be able to retake any modules from year 12 so it's essential you do as well as possible in the AS exams.
Timetabling may also prove difficult if you leave it late to make a decision as schools may have a clash with the subjects you want to do.
Making new friends, the thing that worried me the most as I went to the school I'm at now knowing not one person, will not be a problem. Everyone I've met has been lovely and welcoming.
You'll need to make sure your old head of sixth form will be willing to write and send a reference for your UCAS form if you're going to apply to university as the new school will not know you well enough to write a decent, honest one.
If anyone wants any more advice from me then I'm more than willing to help, just PM me.