I just received correspondence regarding the confirmation of the transfer which is attached.
What’s your recommendation now?
This is just the millionth example of hire companies not knowing what they're talking about. Go back to them:
Dear Hire Company,
I appreciate what you are saying, but one of the legal steps the council must take to transfer liability is to send a notice of acceptance to the registered keeper. From your response, it appears you might have made an assumption, would you instead please properly check your records and positively confirm whether any further correspondence about this PCN has been received?
Yours faithfully,
;D Their system isn’t working now, just tried two attempts to submit a rep and get an error page which is attached.
Send them a letter in the post, keep proof of postage.
Draft representation:
Dear London Borough of Lewisham,
We challenge liability for PCN ZY0648764A on the ground that we do not own and have never owned the vehicle concerned.
Yours faithfully,
In the meantime, contact the leasing company and get them to confirm whether they've heard back from the council since they requested the transfer of liability. If they've not heard back, you need them to confirm this in writing.