For a PoFA compliant NtK to be able to hold the keeper liable, as far as dates are concerned, it must be delivered by day 14 after the alleged contravention. In your case, the alleged contravention was on Sunday 21st January. Unless you have an envelope with a different dated post mark, the date on the NtK says Saturday 27th January. It is deemed as having been delivered (served) 2 working days later. In this case on Tuesday 30th January.
21st January to 30th January is 9 days and so, as far as it relying on PoFA, it is able to do so as far as the requirements of service of the NtK.
You have not entered into a contract by driving on to the relevant land just because they have a sign that states that it is private land. There must be sufficient signs that are prominent enough to be noticeable by the driver. The driver should not need to go searching for a sign. There should be a sign very near where the vehicle was parked.
The driver is not obliged to read the sign to have entered into a contract by conduct. However, if there was no obvious or prominent sign near the vehicle and it can be proven evidentially by photo, no contract could have been formed.
Additionally, the wording on the sign and more specifically the charge for breaching the terms of the contract
must specify the sum and be
adequate to bring the charge to the notice of drivers who park vehicles on the relevant land. In many cases, the charge of £100 (or whatever the charge for a location is) is either hidden or difficult to read in a relatively small font or anything that does not
adequately bring it to the notice of a driver.
You can have a read of PoFA and get your own understanding of here:
https://www.legislation.gov.uk/ukpga/2012/9/schedule/4/enacted