Well ... those who are saying, they need to go into reception for the social aspects - just how well is an extremely advanced child going to be able to relate socially to children of their own age who are just getting started on reading and maths? There is a double bind with the most extremely gifted, where it is very hard to find any appropriate "peer group" - and with your "peer group" is where you usually learn social skills that will then transfer more widely.
If you imagine the 1 in 10 gifted child, there will be at least one in most classes. The 1 in 100, a few in every school. 1 in 1000, will stick out a bit. If you get a child who is academically 1 in 10,000 or 1 in 100,000 - their teachers will generally not have had any experience of a child like that. So yes there needs to be a lot of flexibility in how you approach educating such a child.
I suspect I may have been at the 1 in 10,000 level, and had the added disadvantage of a speech delay from severe glue ear, and being tall enough that if only advancing me had been "allowed" where I grew up, I would have fitted in easily in primary. As it was I didn't master social skills until I found my peer group at university, and only in my 20s did I realise I was a "people person". I have been extremely glad that my own pretty bright / gifted to some level children have had a much more positive school experience than I did. Though it hasn't been plain sailing.
To the OP - if you are being realistic about your child, then look at schools, talk to the teachers, listen to your gut reactions. Then put them in school but be prepared to move them / change how you educate them if it doesn't work out. Some extremely gifted children are fabulous socially and school is really good for them. Others can pick up what they "shouldn't" be able to do and start to underachieve. (my sister was a bit that way).
You may be able to get your child into an independent school on a scholarship / bursary support at some stage, but again you would still need to look very carefully at the school and what they will offer. That's probably something to think about at 6 or 7 at the earliest.
Good luck.