Is it a resit of an exam you missed? If not a resit then you could still meet the offer as you should be able to send off the doctor's note along with a report from your teacher to get an estimated grade from the exam board. I don't know exactly how it works but one of my tutors at college was saying the other day she once had to write a report for a student who was too ill to sit an exam and they had to write about how well they'd been doing in class, what their predicted grade was, who in the class (who did take the exam) would have done slightly better, who would have done slightly worse etc. Then the exam board look at all the info and give an estimated grade from that.
Either way at this point it probably depends on how many applicants they've had and how many unconditional/firm/insurance offer holders they have. If it's looking like they'll fill the course without you then you'll probably get a rejection, but if it doesn't they'll probably make allowances. There's always clearing if you need it where you could get a place, and if not take a gap year and you'll probably find second time round you'll do everything ahead of others applying as you'll want it done and know what you're doing already. I had my firm and insurance choices set by November second time round.