If you tax residence is outside of the UK it will generate more paperwork for the bank and they might decide to close your account. Especially the new banks might not have the infrastructure required to handle that. This is because banks have to report income to the tax country to avoid money laundering and tax evasion.
American citizens have this problem because the US is always a tax residence regardless of where you live so a lot of banks don't want to provide financial service to them. And IRS is particularly bad with paperwork.
If you are thinking of moving abroad, use a big bank like Barclays or HSBC and it shouldn't be a problem.
