The only issue that matters is will you be moving him away from the other parent? If you will it may well be morally wrong to move the child away or the other parent might in that case want the child with them and you h ave to see the child only at weekends when you drive up from Suffolk on Friday night and then drive the child back to London on Sunday night.
I think it is natural when going thorugh a divorce to want a fresh start, often to get away from the pain it has caused, i think my general advice would be not to straight away and give yourself some time if possible to see how you feel once things settle -easier said than done if finances are very tight and i appreciate that.
However, with that said, children can and do change schools all the time (married people move for work and lifestyle all the time) Without being blase, a Reception age child will be pretty adaptable to a new school and new surroundings. ( i moved my own DS at the end of Reception year as we liked another school better) It could be a bit emptional if this comes at a time when the DCs are perhaps getting used to not seeing dad every day and this could add to that, but with your help and stability i'm sure this can be overcome.
You didn;t mention their relationship with their dad? Is it a positive one, do they see him regularly, how would this be maintained with a move, would their dad try to prevent it? For me, i think that is the important thing to consider, rather than a move to new school and area in itself
I am getting divorced at the moment and live in south west London so very expensive. I cannot afford to buy here and rent is about £1500 for a 2 bed. The reason that I am thinking of staying is to make it easier for DCs. DC1 is in reception at a great school with good friends and my job is close by but I am beginning to think about relocating and doing all the change at one. I have been looking at Suffolk where my family used to live and is so much cheaper, could afford to buy. I do not know what to do which will be best for DCs in long run. Any advice would be grateful of.