sounds to me maybe they think you where / are commiting fraud or money laundering. you're accoutn will be frozen and you will be reported for you, there is a very real chance you are under investigation by SOCA and the banks wont tell you shit because they can go to jail for tipping off. if they where closing the account because you where using it as a business or whatnot they would tell you, them not saying anything makes me think its something very serious and going on at them about it won't make them tell you, the fact they are hanging up on you makes me think there is a note on your account saying your a suspect in a fraud investigation or something and nobody wants to get fired/ arresed for letting something slip they shouldn't.

also in regards to record of a cheque not being paid in, banks can see records of transaction you can't - i cant remember if its because they would have reversed it or because somethings been done as an internal transaction to something (i.e moving to a holding account). cant remember off the top of my head its been a few years since i worked in a bank.

if i where you i'd expect the police to come knocking, either politely or with a battering ram.