Do you have a residents association which all owners have to be a member of? If so, does its constitution give it the right to make regulations relating to use of the communal areas?
Have you checked your deeds to see if they contain any covenants or statements about use of the communal spaces? If they do, it is likely the deeds for all the other houses will have the same provisions.
If you can find anything from either of the above routes, there is still the problem of enforcing the provisions. Probably, if there are provisions you can use, the only thing you can do (and it should be done from the other residents as a group) is to threaten legal action. This could be expensive and you would need legal advice. If you cannot find any provisions anywhere then there may be nothing you can do unless the neighbour is running a business and using the parking spaces for that purpose. If this is the case, discuss it with the local authority - who should take action to stop the business use.