Glad to hear you're enjoying your first days in UK.
Looks like you've been busy.

Have your name added to council tax bills and any other utility you can as soon as you have your own place.
Keep trying to get that bank account

The very worst case scenario is to 'buy' an account with HSBC who do a HSBC Passport Account where no proof of address is needed. Not sure how much that is these days.

There are banks out there that can help you. Might try Co-op bank as they used to do a similar scheme but no charges.

Good luck