DO NOT respond by mail, phone, or online. Go into a branch (person to person) to sort this out.
If this is real, and, - you have never been subject to US tax (joint filing with partner), never lived in the US with a US address, nor ever had a green card, ask the bank why they believe you are a US person. If you don't do anything, the bank will assume you are a US person and forward all account information to the IRS via HMRC without further questions.
One line in the letter really bothers me.
"Once we have received your completed form we'll be able to confirm in writing how you will be treated for US tax purposes."
A UK bank cannot confirm your US tax status. All they can confirm is whether or not they intend to forward your account details to the IRS via HMRC.
If having your information forwarded to the IRS does not bother you, and there are no threats of account closures or freezes, you could use the letter to line the hamsters cage - but it's best to sort this out if you are not a US Person.