There has to be a way to find an answer to this, by consultation and negotiation. I would start of by identifying some key individuals, which would be your local councillors at whatever structure you have (e.g. Parish, District, Unitary Authority, and or County) and with your concerned neighbours invite them to a meeting. Your local Clerk to the Council or equivalent should be able to help with that. Invite if you can the neighbourhood Policing Inspector and ask them the question "What has happened to make the situation change, and is there any way that there can be legal parking created.
I have a personal hot issue about people parking on pavements and affecting baby buggies and wheelchairs, but if the pavement is as wide as you say, then it should be possible to put resident only parking bays.
My other comment would be to be persistent. Attend every council meeting and keep asking questions - get the local press involved. Most local councillors do not want to see anything other than good publicity, so there is always an incentive to reach a compromise, if possible.