Hi Happyfrogger, I know quite a lot about admissions from an appeals point of view (I sit on the panels), so hopefully between that and the SEN point of view, you'll get a useful answer, because it's quite complicated.
Ok. So, your DD, if she gets a statement (EHCP by then), will be taken out of the admissions process, in that she is guaranteed a place at the school named by the LA in her statement. So far so good.
If she doesn't have a statement (EHCP) by then, she will be subject to the normal admissions process. Each school at a minimum, must give highest priority for Looked after Children/Previously looked after Children.
Other than that, no school (LA) has to have a particular set of criteria. That means that they are free to take into consideration Social/medical issues, but equally free not to.
If they do take them into account, then the Admissions Code says:
"Social and medical need
1.16 If admission authorities decide to use social and medical need as an oversubscription criterion, they must set out in their arrangements how they will define this need and give clear details about what supporting evidence will be required (e.g. a letter from a doctor or social worker) and then make consistent decisions based on the evidence provided."
The bar is set very high for most LAs who use social/medical criteria. The letter accepted normally has to say that this particular school is the only school that is suitable for MiniHappyfrogger because of x, y, z. The alternative is to have a letter which says 'MiniHappyfrogger must attend a school within 3 minutes walking distance, which has x, y, z facility', where the only school that has that facility in that distance is the one you want.
Anything vague or wishy washy, such as 'Happyfrogger tells me that her DD would be best placed at x school and would be much more reassured if she was there' or 'Happyfrogger feels.....' will be thrown out. It has to be the opinion of the professional that is stated, not a report of your opinion.
Also, in general, a GP letter won't carry much weight - they get hundreds. It would need to be a Consultant, named social worker, etc.