It depends how they do it.
If they keep you as an employee but merely put you on gardening leave, you are essentially still on the payroll but not required to do anything - so you keep the car til the end date.
If they terminate your contract early, you should be offered a payment at least equivalent to the salary and benefits you would have received, in compensation for the contract breach. There's a bit of room for negotiation here, because they are contractually obliged to pay your full salary and benefits, but you can benefit because they can pay you the sum gross - it is not salary so not subject to pay or NI (or employer's NI for them). Under that deal you won't normally be allowed to keep the car for a month as there may be an insurance issue, as you are no longer an employee.