DS2 went for assessment at age 5 at 'prep'school where DS1 was. The headmaster doing the assessment said he would take him but he would struggle. By year 2 we relaised he was dyslexic/dyspraxic, the school was giving him extra support by fully qualifed Spld teacher so no problem there and he was having occupational therapy outside school.
However, these schools specialise in getting 11/13 year olds into the best secondary independant schools via common entrance. This type of eduction IMO does not suit a child with learning difficulties, however bright - DS2 when tested has IQ of 138 on verbal/cognitive side.
We left DS1 at the prep school who went on to get into and is currently thriving at one of the best schools in the country. We removed DS2 to a special school for 3 years until he was ready to go back into a 'sympathetic' mainstream school.
At this special school the headmistress had a great deal of experience on where to send them next. When state school was discussed, her opinion (this is london BTW) was that although there is provision for dyslexic pupil which can be more extensive than at private school, they tend to put these kids in the lower streams amongst kids with other more extensive problems and the class size doesn't help either.
DS2 currently in year 8 at a progressive private school as a weekly boarder(his choice). He is in the top set for english as his intellectual ability is recognised even though very little of it gets down on paper. Other teachers rave about his general knowledge of current affairs etc but have to spend time deciphering some atrocious handwriting and spelling.
I don't know what will happen about GCSEs as simply passing a maths one is going to be a struggle.
I've got off the point here a bit, sorry. But I do feel strongly that if you can afford it, the right private school with the right support is the route to take.