To expound a bit on renouncing:
US citizens have a right of expatriation (renunciation). As long as you meet the requirements, you can renounce.
The requirements are stated in Sec. 349. [8 U.S.C. 1481]. Relevant bits:
"(a) A person who is a national of the United States whether by birth or naturalization, shall lose his nationality by voluntarily performing any of the following acts with the intention of relinquishing United States nationality-
[..]
(5) making a formal renunciation of nationality before a diplomatic or consular officer of the United States in a foreign state, in such form as may be prescribed by the Secretary of State; "
The Consular Office has a duty to consider whether the individual is acting voluntarily (i.e., not under duress). That's all. The Consular Officer will form his/her opinion based on the forms and documentation submitted by the individual. There will be no questions about IRS compliance.
The Consular Officer takes your money, administers the Oath and sends the forms and documentation to Washington, stating his/her opinion as to whether the loss of citizenship should be approved (i.e., the person is acting voluntarily). Eventually, a CLN arrives. Job done.
Consulates differ in the documentation they ask for, and in the time it takes to get an appointment. Check the website of the desired consulate/embassy for further information.
Once you've renounced, give your bank a copy of the CLN and sign their self-certification form (certifying that you are not a US citizen). That's all they want. They keep it on file, and it proves that the bank does not have to report your account to HMRC for forwarding to the IRS.
FATCA/IGA has been incorporated into UK law. That makes it a potential problem for anyone born in the US, because anyone born in the US is a potential risk to a bank. Advisable either to show them that you're not a USC, or to confirm that you are indeed a USC and sign the W-9 and give them your SSN.
US tax law has not been incorporated into UK law. Once you've renounced, if you have no US assets or income, you're no longer tax-resident in the US and can prove you're not tax-resident in the US, so FATCA/IGA is no longer a problem.