Parking incorrectly was (and in some areas remains) a criminal offence, dealt with by the police (or traffic wardens and.or PCSOs working on behalf of the them).
However the Road Traffic Act 1991 gave councils the power to apply for the decriminalisation of routine parking offences within their areas, making the parking violations civil matters, dealt with by 'penalty charges' rather than 'fines. Where that has happened, the police no longer have anything to do with routine parking enforcement (although they can, of course, still prosecute drivers for criminal offences such as obstructing the public highway).
Your local councils have taken up the option to decriminalise parking violations, so the police are no longer involved. Control has passed to the Shared Parking Service, whose address is
Parking Office
PO Box 238
Havant
PO9 9EA
(Tel: 023 9244 6019).
If a vehicle is parked "with one or more wheels on any part of an urban road other than a carriageway" (e.g. on a footpath, cycle path or verge) a 'Code 62' Penalty Charge Notice can be issued:
http://www.newparkinglaws.co.uk/post/PCN-Contravention-Codes.aspx
If the path forms part of (or links into) the Hayling Billy Trail, it was probably partly-funded by the charity Sustrans. They welcome feedback about the routes they help to develop, and will look into any problems associated with their use:
http://www.sustrans.org.uk/
Chris