Sorry for the long post but I was in a similar situation and also have DS1 in state school and DS2 in independant pre-school.
My DS was very advanced at 2 and taught himself most things (not as advanced as yours Blossom though). He is at a very small state infant school , he was in a class of 15 in Year R and is now in a class of 20 in Y1. To some extent I think all schools are able to provide individual support for all children but maybe not as much as in a private school as often the classes are just too big. Also discipline is VERY different in many private schools to state school.
I am shocked Learnandsay that you feel you need to be doing so much educational stuff at home for your DC at home at such a young age but maybe you have given the wrong impression of what you do and maybe you are just going along with what DC wants to do?
My DS is still doing really well and is achieving a year above his age all ronud, when he started in YR he started on a Y2 reading level and has continued to progress well and has been assessed as an overall 2a in Literacy a few weeks ago so is well above average but not exceptional (according to MN as many children are level 4 at this age apparently!). His reading age for just words is 10 1/2 so nearly double his age but obviously there is difference with his comprehension - something people often forget with their DC!
I do still have thoughts about what his achievements could be if he was in private school as for instance his current school spend lots of time getting children to the average level (ie 1:1) but no time with the higher achievers as they do not need to. In a private school there should be a lot of individual work, in fact when we looked round they showed me the bottom child's reading book and the top child's reading book in a Y1 class of 16 boys and they were 'years' apart. One was still a very basic reading book, the other was Harry Potter! The other thing is the variety of work- ie lots of sports, music and languages from the age of 4 so a good rounded education.
I left it too late to get DS1 into the independant school at infant level as we wanted to be sure we could afford it right through to 16 but he starts there for Juniors. DS2 is already in the pre-school and starts the infants in September.
Some of the other private schools in the area are snobby and ridiculously expensive, the one we have chosen is non-selective, very family orientated, less expensive and small. We are happy at the state infant school at the moment but the HT left this year and a new one has not been appointed yet so things may change.
Same advice as the others though, look around, ask lots of questions, some schools 'dislike' bright children, I have experienced it myself, with my DS and also with other peoples DC. Bright children (and their parents) can be a 'nuisance' to some teachers whereas other teachers love having a good variety of abilities in their class! I don't think a G&T programme is essential in schools necessarily as good schools should be able to differentiate well!
Also, don't forget you can always leave the basic literacy and numeracy to school and broaden your child's learning with things like chess, languages, musical instruments or something likedrama/dance!
I hope you find somewhere suitable!