I can't think of any reason why having your mail re-directed should, of itself, be regarded as illegal.
If, however, there's a particular reason why you're seeking to convince the bank that you're living at your old adddress, that reason might make the action illegal. If, for example, your old address was a property which you used to own, and had been used as security against a loan (which you've not yet repaid) then, by not informing the bank that you've sold the property (and left them with no security for the loan), you could be charged with 'seeking to gain a pecuniary advantage by deception'.
So, what you need to remember is that it's not, per se, an offence to deceive someone. It is, however, an offence to deceive them if, by so doing, you seek to gain financially by the deception. Without knowing why you want your bank to think that you still live at your old address, it's impossible to give a definite answer to your question.
Remember, anyway, that there's a maximum period of two years for which the Post Office will redirect your mail from your old address.
Chris