Hi,
I'm one of the student ambassadors here at Coventry University,
I've not been in this situation however I do recommend potentially getting in contact with your universities dispute team and seeing if there is anything that they can recommend you to do, especially as you said, you have proof that the university accepted your request to move on the first come first serve basis. This evidence is a great thing to have in this situation.
I'd recommend doing some research about how to get into contact with the dispute team and go from there. If they aren't able to help, they could be able to point you in the right direction.
I apologise that you're going through this, I could imagine how frustrating it is.
I hope this gets sorted for you soon!
Kind regards,
Courtney H