Worst case scenario: They say no. Nothing else. => Try! Do it now, it is better early than late and make sure, that you contact the universities before hand, just because it will sound better, if you contact them before and not only in the case you have missed your grades. That makes you more credible, although as long you have your claim backed by evidence it shouldn't make a difference. Another advantage would be to be prepared, which gives you one worry less during exams.
See that you get a stale surrounding with people caring for you and avoid thinking about some comments of others and you have the right to ask for allowances!!!
And just at the end: A deferral isn't the end of the world and might be better in the long term. A gap year between sixth form and university is more likely to benefit you than harm you and nobody takes care of it. So take all the time you need to recover, get back in a state of mind you need to get the best out of your studies!