The basic fact is that by not updating your V5, the situation is entirely of your own making, sorry to have to say it. So in view of the amount being demanded, my recommendation is that you pay-up before the bailiffs visit and add on a visit charge. Paying the bailiffs is entirely separate from the process described below and has no influence on it.
There is a process to revert the matter back to the PCN stage, which is to submit an Out-of-Time Witness Statement to the Traffic Enforcement Centre, (the "court"), that you didn't receive the enforcement documents. The only problem is that being OOT, the council will be advised of this, and can object to the WS being granted. TEC will then refuse your OOT WS. You can ask for a county court judge review, but this costs over £100 for a papers based review, and around £270 for an interview with the judge "in chambers". If the juge confirms the refusal decision, the fee is not recoverable.
We see quite a few cases like yours on his forum, and the truth is the outcome is rarely favourable, because most people have just forgotten to update the V5. When did you move address, and when did you finally update your V5.