I can talk about St James as DD is there in year 7. But FHSS is popular here, so hopefully someone will come along and post about it.
It's only been a few months there, but so far we are very happy with St James.
Good induction at the start of the year, girls went on a team building trip together, and DD made friends fairly quickly. Plenty of clubs available to find people with common interests. According to DD, teaching quality is excellent. On top of the usual academic subjects, girls do cookery - very popular, and sewing.
They do frequent assessments, track and intervene quickly if needed. For example, following a test, some girls maybe invited for subject clinics, and/or will retake tests following some work. Homework is about an hour each weekday, and bit more in the weekend.
Among the unusuals - quiet time between lessons, which I think is a brilliant idea, but DD and her friends are not fans. Good range of options for veg lunch available but also not very popular among DD and her friends at the moment(I hope they will come around these over the years!)
About your specific query on learning support, afraid I don't have much details - I know the school has a higher share of children with mild to moderate learning difficulties compared to other selective indies in this part of London, (Good School Guide says about a quarter). But beyond that I don't know what learning support they provide. They have an offer holders day tomorrow I believe, so this question might be worth asking there.
Good luck with your school choice, and well done to your daughter! Both are very good schools, don't think you can go wrong with either.