Sorry you have been unwell and I hope you feel better soon.
Sorry you are in this position too.
One of the things about this for me is that as far as I can see from what you wrote, they suggested to you that you could defer or write to them to ask if you could defer.
And this gave you some kind of expectation that they would agree to you deferring, and as a consequence you didn't take the UCAT as you didn't think you would have to reapply? I don't know whether it was right or not to make this assumption or not, but is what happened.
And now as a consequence of this, its not just that you have lost your deferred place but also the possibility of applying elsewhere.
It sounds really really harsh when written down like that. I don't mean it to be, but it's the kind of point that I would be making in my appeal.
The main issue however is the reason for the request for a deferral and making absolutely sure you know the deferral/admissions policy and ensure that they have all the information they need to assess your appeal against their policy 😉
Good luck with it 🤞