The gov.uk guidance dated 6 January states:
"Public outdoor places include:
- parks, beaches, countryside accessible to the public, forests
- public gardens (whether or not you pay to enter them)
- the grounds of a heritage site
- playgrounds"
No mention of parking charges. So that's a red herring.
We don't have much of a constitution but what we do have is "What the Queen enacts in parliament is law". No mention of what the police or someone on a parenting forum fancy. The law comes from parliament.
If you receive a fine from the police you have the right to contest this in court. Not being bothered to or being afraid to use a facility available to you does not make the system unfair. I have friends who are magistrates and nothing elicts an eye roll like asking them about these police-issued 'fines' for not breaking the law.
Those of you who think that it is right for the police to decide for themselves what's legal and what isn't, or 'interpret' the law, might like to bear in mind that while the 'laws' that the police are inventing suit them at the moment, the day may come when they are accused by the police of breaking the law when they are doing something perfectly legal that they may very much want to do. The principle holds in all circumstances, whether they suit the individual at a particular time or not.
If you support the discouragement of people from breaking the guidelines, by all means encourage the police to ask them politely to desist, but we should all, including the police, remember that the public are quite within their rights to thank the police for their advice and continue with what they are doing. The police had better have a darn good reason for trying to 'enforce' guidelines.