It's extremely unlikely that Imperial will change the offer. You can still be entered for resits, but you might end up paying a lot.
Also, are you certain the offer doesn't require you to get the A grades without resits?
Try entering privately at another centre for C4.
you've told your school this and they won't let you enter a resit? wtf? if that's the case go to another college/school and do it there instead.
You can fill out a form to do a resit - it will just cost a bit more! Then if you get over 80 it should replace the lower grade you got last week?
They only say you have until XX to send in a form so that no-one tries to give one in last minute or something.
The resit deadline hasn't actually passed, even if your school's has. Your school will still be able to put you in for the exam. The exams administrator might be a bit pissy but, frankly, it's worth it.
Make sure your offer doesn't say anything about no resits though, otherwise you're really just wasting your time.