I am very on your behalf, and completely outraged...
But, I would seriously consider changing schools. You say he has settled into school well, but you also say that every day he asks when he can go back to Reception...
It is only 6 weeks into many many years of schooling. A few children I know have just moved schools when a place became available.
I have no idea what repeating Y3 is going to do to your son. But, they have pulled him away from his friends now, and he will spend the next 4 years making new friends, only to be pulled away from them when he has to repeat Y3.
My ds is in Y3, and to be made to repeat Y3 when all his friends move up would really really upset him. Just remember, when your ds is in Y3 he will be 7 and much more attached to friends then he may be now... Also, the current Reception class will by then have made firm friendships, so how will your ds fit back into this group??
If it was my son, I would move him. One move, made whilst he is so young he will easily make new friends.
In addition, I would be soooooo angry with the head of this school, I would never want to set foot inside her school ever again. Even if that means cutting my nose to spite my face....
Sorry if none of this helps you, but I am just sooo sad and outraged that this can be allowed to happen...