Answering the call from HotpotLawyer!
we are on the border of 3 LA's so two closest schools are in different LA to where we are and we have been told preference given to pupils within authority.
As others have said, this is illegal. They can have a formal priority area, the boundary of which coincides with the LA. But, if they do not have that and decide admissions based on distance, they absolutely cannot prioritise pupils with the LA. Complain. Loudly. If they say they are acting legally, mention the Greenwich judgement (this was the court case which established that LAs cannot prioritise pupils from within their own area). If they continue to resist, tell them that you will refer the matter to the Local Government Ombudsman. And definitely appeal, although that really shouldn't be necessary. From the information you've posted it sounds like they have made a clear mistake which they should correct without going to appeal.
If you want to PM me the name of the schools and LA involved before you complain I will be happy to take a look and make sure you aren't missing anything.
hypothetically if the over subscription criteria has been applied wrong, this is likely to affect more than just flippy, (and then the downward ripple effect as well) can offers of places be withdrawn to those who otherwise wouldn't have got in?
Offers can only be withdrawn if they do it very quickly. There is no recent case law on this but it is generally accepted that they have to withdraw offers made in error within 3 days. If they don't withdraw the offers and the school really can't cope with the additional pupils who should have been admitted, their most likely way forward is to make the affected parents appeal. The appeal panel will then have to figure out how many the school can cope with and which children are most deserving of places.