I remember having a similar problem with my bank, I'd lost my bank card and needed money for food... having neither a driving licence, nor passport I went through a few of their security checks and finally the lady behind the counter asked me for my signature. I signed the slip. She looked at it and back at the screen and replied I'm sorry the signatures don't match. So I resigned it a bit more neatly and a bit less in the style of, "I sign a few hundred forms a day". Still the signature didn't match. Now, believe it or not I know what my signature looks like, she apologised profusely bt said that the signatures still didn't match and bank policy at the time meant no money.
Keeping my cool as much as possible I asked if I could possibly see a manager, a couple of minutes later a manager appears, there's quite a queue by this point as there are only two windows open. I explain the problem to him, I tell him I appreciate that the lady can't help me any further and I'm hoping he can exercise some discretion as I have satisfied all of the other security requirements.
The chap asks me to sign the paper again... part way through I pause, ask for another slip and sign it the way I did when I opened the account at 15 and ask if that is a match. They both brighten up and say that's exactly it... at which point my face (as my friend described it) looked like a thunderstorm was rolling in. Three years after opening the account, my signature was no longer the same and I submitted a change of signature form. Now five years later I find out that despite having a form confirming the signature change they had never changed it. In a slightly louder voice (as I was getting a little stressed at that point and I wanted to make sure the other customers overheard), I asked if they had not changed my signature, why were any of the couple of hundred cheques I'd written authorised? "Oh we only spot check cheque signatures, one in every few thousand or so". Cue explosion, white faced manager stammering that he can certainly authorise me to withdraw any ammount I like and will personally see to my signature change, perhaps I'd like to step into his office and would like a drink while things are being sorted out?
So all worked out well in the end and any time following that the bank needed to confirm my identity after that I simply used to get them to bring that manager down as he would vouch for me.
However now I'm in a new city I'm having these issues again, more to come as I've just noticed my provisional expires at the end of May, time to find my passport, lol.