if it is a private road there is probably no reasonable way for parking to be either permitted or prohibited. Parking on the public highway is controlled by traffic regulation orders (a legal document that states what controls are on the street). It is this that forms the basis upon which parking enforcement can be made. On private land it would be a civil matter.
If people have been parking there for years I would doubt that they have a right to do so simply because they have been doing so for years. However I understand that there are rights of access gained on the principle of there being permitted access for a time, so there may be something similar for parking, but I would doubt it.
if the land owner wants to have access off this lane to a development site he will probably need to demonstrate in his submission to planning that the site can be accessed safely from the public highway via his lane. This will usually mean that two way traffic can move through the access (usually requiring about a minimum 4.8m road width, and that visibility is unobstructed by parked cars. Also there will need to be enough room for a refuse vehicle to get in and access the properties….lots of parked vehicles may be a problem for all of these!
if the access is going off his lane rather than off the public highway it would be unlikely that the new roads for his development would be adopted by the council. If the council were to adopt it the private lane would also need to be adopted, which would mean the developer bringing that road up to adoptable standard….making it more expensive and complicated for them.
If they have submitted a planning application already you can have a look at it via your council’s website (usually called something like ‘planning portal’).