I received one of these also, I wasn't surprised as my account with them is 20 yrs old, so wasn't surprised they were looking for up to date ID. In my work I have at times also had to send these letters, financial institutions are required to prove they have verified the identity of their customers in line with Anti Money-Laundering Regulations.
I understand people being cautious though, if concerned you should always phone the bank to make sure the letter and return address are bona fide