That is not what I heard. After renouncing US Citizenship, getting a visa (or an ESTA) won't be straightforward. Of course it's possible, but it will be something the consular office will analyze carefully.
On your motive, i.e. the issue with the UK banks,: can't you find a small bank in the UK that does not ask the question if you're an US person? Of course you would have to continue to prepare your US tax return and the FBAR and report any international bank accounts, but it would make your life easier with the local bank.