Any major expense should be agreed at a leaseholder's meeting. Subject to this, most leases give the management company the power to either share the cost between everyone or just between the flat(s) concerned.
My opinion is that, if this is a major expense, you should put your case (or you should already have put it) at a suitable leaseholder's meeting and you should accept the result of any vote irrespective of how your own vote was cast. If it is not a major expense, you should pay up and, perhaps, suggest that some work is done in the future to benefit residents who do not use the parking places (better pedestrian access, perhaps).