From what I understand, in principle UK banks dont want customers who are non resident, principally because of the onerous regulations they must comply with regarding money laundering and tax evasion. I’ve read of a number of examples of Brits who have had UK accounts for many years, receiving letters, asking them to withdraw their funds. If you are a US resident, you stand no chance, as the US reporting requirements are excessive and not worth the hassle. About all I can suggest is you think about say HSBC Jersey, which is about as close to having a UK bank account, as you will find.