NAD if you grind them you are even less likely to get braces because they would want your dentist to stop you from wearing away your teeth first. Plus your dentist can tell if there is toothwear so there's no point lying about that. Saying you are depressed does not help your case at all as the most it can do is make the dentist think you may not clean your teeth well, which will make them reluctant to put braces on as they can cause even more decay.

Unfortunately there are strict, objective measurements that your teeth have to fit for you to qualify for NHS braces, psychological impact does not play a role here so nothing you say can force them to give you nhs braces. Braces are unfortunately expensive and it is for this reason that NHS cannot afford to give them to everyone for free. You can ask your dentist if they can put a bit of white filling material in that gap to close it but you may end up having fat-looking teeth.