Monzo will do this; I signed up for a bank account without a permanent address, and had one within 30 mins of arriving in the UK. They still require an address

Monzo will do this; I signed up for a bank account without a permanent address, and had one within 30 mins of arriving in the UK. They still require an address to mail you your card (so not the same target market as the OP), but it wasn’t too onerous.