Not legally, according to my research (we run a UK Ltd). But it sucks a bit to not have a UK bank account, because for HMRC (tax office) we could not click next in an important dialogue until we entered a bank account to which tax repayments are to be paid out in the UK specific format ("account number and sort code"), which you only get with an UK bank account. This was 9 years ago.
If you open a UK Ltd fully remotely, you can get bank accounts with Wise and Revolut. Don't take only one of them, always have 2 banks. Because e.g. Revolut randomly held a medium sized customer payment (one of many, from the same long term customer) in lock for months for no good reason. We could not talk to a human to resolve it. Never rely on a single bank.
If you open a UK Ltd fully remotely, you can get bank accounts with Wise and Revolut. Don't take only one of them, always have 2 banks. Because e.g. Revolut randomly held a medium sized customer payment (one of many, from the same long term customer) in lock for months for no good reason. We could not talk to a human to resolve it. Never rely on a single bank.