OK, so Mr Mustard has (as usual) come forward with a trump card! The PCN seems to have been served too late and so Havering cannot (legally) pursue you for the penalty. That should be enough to win it for you on its own.
Only trouble is the most recent letter suggests Havering believe you to be beyond the point of making any representations and we are a bit in the dark as to why. Can you seriously not recall at all how and when you responded to them? I presume you sent representations using their online portal? Did you take a screenshot of what you wrote? Anything at all to indicate what day it was?
Hopefully, it is as simple as writing to them to point out they served the PCN too late. However I suspect they will ignore/refute this, or fail to understand the concept of service (after all their recent letter implies they believe the PCN was served on 18 October). In which case you will have to somehow get the PCN back on track of the formal process. If they have issued a Charge Certificate, then the next stage is an Order for Recovery which includes the means to get the process reset if you can confirm you submitted representations in time and did not receive a Notice of Rejection.