I do not reside in that county so unfortunately cannot help with schools in that area. Presumably he will go to an infants school in the state sector?.
Go to each school in advance and ask them what their experiences are in educating children on the ASD spectrum and how many of them are statemented. Meet with the SENCO (special needs co-ordinator) and ask that person plenty of questions.
Does your son have 1 to 1 at nursery; does he have any additional funding allocated to him specifically?. This won;t necessarily be transferred to Infants; this is why you must act asap.
I would seriously look into obtaining a Statement of special needs for your son from your LEA asap. That is a long process; even if straight forward a Statement can take six months to set up.
You do not need anyone's permission to do this and you as parents have more clout than school would have if applying for such a document. For a start you can appeal if the LEA say no, the school cannot. A Statement is a legally binding document outlining your son's additional needs and how they are going to help him in terms of extra support given to him in school. Other plans like School Action and School Action plus if mentioned to you are limited in scope and are importantly not legally binding.
A Statement if obtained will make the school more aware of his additional needs both educationally and socially. Applying for such a document now would be easier than say waiting until the end of his reception year or even later than that.
You are your son's best - and only - advocate. Never forget that.
IPSEA are very good at the minefield that is the Statementing process and there are letters on there you can use:-
www.ipsea.org.uk