Painful I know, but the sad fact is that you appear to have signed an acceptance for which is your agreement to the terms and conditions of the school. Sounds like you may not have read them in full - never a good idea! The clause you mention is common place. It is certainly not worth your while spending money on lawyers concerning this, but you may get somewhere if you write to the Head teacher of the school setting out your dismay, saying that you understand you will lose your £250 as this was explained, but that the contract clause was not pointed out to you even though you accept you should have read the terms yourself. In a situation like this where, however unfair you feel it to be, in legal terms the school is in the right, appealling to their better nature may be the only way forward. You may want to mention the fact that it wook them until October to send a bill.
In terms of finding out who registered when and if the school is full for reception (which would mean your place was certainly filled), all you can do is ask the school directly. They do not, of course, have to tell you this.