In theory, it sounds like it searchlight, but in reality I doubt it. They could argue that your overpayments hadn't been sitting in their coffers collecting interest, but'd been spent on admin, for instance.
It's like when British Gas gave everyone "free" lightbulbs not so long ago. They would've got them at a fraction of what you'd pay for them in the shops, but even so, with all its customers, it must've cost - and wasted - quite a bit of money. I imagine you'll be refunded - but literally by the the amount they charged you in error. Might be worth asking about though!!