From the available council information, the penalties specifically for illegal parking in green spaces are not detailed. However, there are general enforcement rules, including Fixed Penalty Notices, that can apply to various offences within parks and open spaces.
For example, regarding dog-related offences, individuals can receive a Fixed Penalty Notice of £100 for breaches. It’s possible that similar fines may apply to illegal parking, but specific details aren't provided.
If you have concerns about illegal parking in green spaces, it might be best to report it directly to the council for clarification and potential action. You can find more information about environmental issues here.