Follow all the advice above. I would fully expect Shire Hall to put their hands up and say 'sorry' and recreate the form once they hear you have proof that you sent it.
If the worst comes to the worst, you'd find an appeals panel would be very impressed by the evidence you submit - i.e. the S.E.A, and an appeal would be allowed on that ground for whichever school your child would have got into had the LEA not lost the form. That doesn't mean the number one choice if you wouldn't have been allocated it anyway, nor does it mean a grammar if your child wasn't successful at the 11+!
You can remember what you put on it, can't you?