Thanks all for the info and counsel.
If the IRS gets info from the UK about US citizens who may be concealing income etc does HMRC get anything in return, I wonder? Or is it just a one way street?
US banks, and banks in the 100 or so countries which have signed up to the Common Reporting Standard and Automatic Exchange of Information, are required to record your tax residency. If you tell your bank you are tax resident in the UK, they will report the
relevant data to HMRC.
However, currently it is all self-declared anyway. Even though in most countries it is likely to be an offence to make a false declaration, there is no real way for banks to verify your tax residency. In particular, determining UK tax residency can be very complicated especially in edge cases.
So if you don't tell your bank, or you declare that you are not tax resident in the UK, they won't report that information to HMRC, particularly if you are a citizen and/or resident of the country where that bank is located.
In the other direction, since all US citizens are liable for US tax, it is easy for non-US banks to know whose details to report to the IRS, but if you don't live in the US, were not born in the US and have another citizenship, it is possible that a bank will not know and not think to ask.
Furthermore, FATCA is a separate thing and non-compliance can threaten a bank's ability to trade in the US. Evidently, given the number of Americans (including multiple-citizen Americans) who have UK accounts, many UK banks have decided that they should proactively ask customers to inform them of their US status, rather than just waiting for customers to voluntarily provide information.
Nonetheless, you can probably ignore the request unless/until Halifax threatens to close your account for not responding. I have not yet been asked to fill in such a form for my Halifax accounts myself, but they have sent me several communications which included a sentence about being required to tell them if I have any US status (which I don't).
Also, my Halifax app recently asked me to confirm my personal information was correct. The information included my citizenship, income and expenses. For Halifax, it was possible to skip this, but other UK banks have also asked me to confirm my citizenship and other information (without mentioning the US) and it was not possible to continue accessing their app/website without confirming it.