The short answer, explained
HMRC can look at your bank account, but only through a formal process. It cannot simply browse your banking online or ring your bank for a casual chat.
It must use a Schedule 36 information notice, either addressed to you directly or as a third party notice sent to the bank itself. The notice has to be specific about what records are wanted and why they matter to a tax check.
For a director, this usually surfaces during a self assessment or corporation tax enquiry once HMRC suspects income or expenses have not been fully declared.

