This thread really helped me when I was looking for lessons for my daughter when she had chronic fatigue syndrome (age 13-14). So even though it's pretty old, I thought I would add a few hopefully helpful comments for anyone else desperately wondering what to do about their child's education.
After giving up with her secondary school who were unable to help her much, we tried out a private tutor, Briteschool and we eventually ended up at Interhigh during 2014/15.
For children who cannot access mainstream school but are reasonably motivated to learn and can concentrate in a structured environment for a few hours a day, Interhigh provides a great alternative. The lessons are (nearly all) of high quality, the teachers are enthusiastic, organised and responsive to individual needs/requests, the admin is efficient and the timetable is usually quite flexible. My daughter took Year 10 in most subjects and Year 11 in 2 other subjects, which enabled her to feel less frustrated (which she did at her previous school) at sitting through stuff she already knew. Although already conscientious, at Interhigh she has learnt how to study by herself and write 'proper' essays in a way that school did not manage. She sat the 2 iGCSEs this summer and is feeling confident about the results - Interhigh are very focused on exam preparation/support in these 2 year groups.
It is very good for children with chronic fatigue or other illnesses, because if you are not feeling well, you can just listen or if very ill or you have to go to medical appts etc, you can catch up using the slides in the lesson library (there are now also more recorded lessons there). The core timetable is approx 3 hrs/day and the structure/daily human contact means that you still feel part of something and have done something useful/fun, rather than staying at home feeling ill and knowing that you are getting more and more behind and out of touch from a bricks'n'mortar school.
The main downside (apart from cost - approx 2400 per year) is the difficulty of making close friends. Although everyone is very friendly/open-minded and there is a lot of text chat but it is not the same as having local friends.
Not sure if it is possible on this site, but happy for anyone to pm for any questions.