Redfraggle you would not automatically be entitled to a perk which happened to come with one office if you relocate to another office, no.
Office space with unlimited parking is a luxury indeed for an employer, so as catweazle illustrates, office moves that involve giving up this perk are commonplace.
How are employees and managers communicating about the move? Are there discussions in progress? If you have a union I am sure they are involved, if not is there some kind of staff association or other mechanism to represent concerns of the staff?
Obviously travel arrangments to a new office are always of prime concern to employees when relocating, so ideally as part of the move, your employer should be considering various options to make this easier, and employees/employee representatives should be helping propose and discuss those options.
Is any of that happening? Options often include car sharing, this can be very organised if done properly and can take into account people's different circumstances. Other options off the top of my head might be a shuttle bus from the nearest suitable car park or train station if buses are not good, more working from home on a rota basis, priority given to some groups of staff, or everyone being able to park some days each week.
Your best bet is to make sure that employees' concerns about the parking situation, and any other concerns about the move, are being heard and addressed properly, and all alternatives being explored.