So they are wrongly claiming the ability to hold you liable as the keeper. You should in due course complain to them about that, which we can advise on.
In the meantime, the first thing to do is appeal.
Don't do this until Tuesday 8th April. Dear Sirs,
I have received your Parking Charge Notice (Ref: ________) for vehicle registration mark ____ ___, in which you allege that the driver has incurred a parking charge. I note from your correspondence that you claim to be able to hold me liable under Schedule 4 of the Protection of Freedoms Act 2012 ("The Act"), but this is not true. You have failed to deliver the notice within the relevant period of 14 days as required by paragraph 9(4) of the Act.
Date of parking: 23/03/25
Date of issue: 03/04/25
Date of presumed service under 9(6) of the Act: 07/04/25
Days elapsed: 15 days
I am appealing as the registered keeper. There is no obligation for me to name the driver and I will not be doing so. I am therefore unable to help you further with this matter, and look forward to your confirmation that the charge has been cancelled. If you choose to decline this appeal, you must issue a POPLA code.
Yours,
If appealing online, be careful there are no drop down/tick boxes that cause you to identify who was driving, and keep a close eye on your spam folder for their response. If they do not respond within 28 days, chase them.
But as above, not until 8th April!