Hi toby. I did change schools when I was about that age. And honestly, I hated it. I still remember it vividly, starting afresh, making new friends, and I had some kids that would pick on me and make my life a bloody misery.
This stuck through me all my adult life, and I vowed if I had kids I would never change their schools. So when my marriage ended and I moved out of the area, I still continued to drive my children to their schools (a 30 mile a day round trip).
I did take my youngest 2 out of their previous school in 2006 and moved them to a local one, as to be honest, it was tiring, and I was working, and I had been doing this long school run since 1998! And I just could not do it anymore.
I felt very bad about it, but they settled in very well into their new school. Made lots of new friends, and part of me wish I had done it sooner. But I guess my past experience made me scared to.
Sorry for long winded response.