Yes, but only if you give them a really, really good reason. The Department for Work and Pensions isn’t sitting in a dark room, monologuing, “Behold! They bought a second packet of Hobnobs!” They have better things to do. Like, presumably, filing paperwork on other paperwork. They cannot just stroll into your bank for kicks.
Think of it like this: the DWP is a grumpy bouncer at a club. They can’t search your pockets unless you start a fight (or claim benefits you’re not entitled to). For 99.9% of people, your bank account is as private as your Netflix watch history. But that 0.1%? Oh, they’re the reason this article exists.