In reply to Baron Weasel:
HMRC can be a PIA to deal with or sometimes they can be sweet reason itself.
It is, in fact, their problem, and it's not very hard to understand: there is a thing called RTI now which means that HMRC have been informed in real time what you were supposed to have been paid and what tax etc has been deducted. If what they reported is different from what you received then this is not 'iffy tax' it is fraud. (Probably committed in circumstances of extreme stress but sitll, you shouldn't be bearing the consequences and they shouldn't have done it.)
This is an HMRC/police matter. Speak to HMRC, say you believe fraud has been committed, and ask who to report it to. It is THEIR problem. Always ask for a reference to the call and the name of the person you are speaking to,