Year 11 is a terrible year to be moving schools under the UK system as most GCSE courses are taught across 2 years and this is the second year. Even if there was an available place in a school, the odds of them following the same course content that she has covered in Year 10 is not great given the various different exam boards and choice of set texts etc.
If I had a child in that situation, I would personally leave them at their current school for Year 11 if I could possibly do so. When I was 15, the father of one of my friends had to relocate just as she was about to start Year 11 and she lodged with one of our maths teachers during term time to avoid disruption.