https://www.buckingham.ac.uk/education/pgce/independentpgce
I found this course at Buckingham University which offers an iPGCE (a PGCE specifically for Independent schools). I know a number of people who did this course and really rated it, especially as you get to complete the course remotely whilst working in a school of your choice. This allows you to gain some really good first-hand experience of working in a school whilst learning about teaching.
