The legal answer is that it is going to depend on what your contract of employment says. Not just the bits of paper received by you over the time you have been employed, but also the published policies by the company that have become part of your T&Cs of employment.
You are still an employee of the company, so if you can find that it says you will be provided by a car as a benefit, and there ISN'T anything in the sick pay scheme details that says you will only receive SSP (and no other benefits) after x weeks paid sick leave, then you are probably home and dry.
Having checked out what you can, I would broach the subject with the employer. At the end of the day, if you are a valued employee it is perfectly OK for them to agree you retain the car over this period - even if technically (legally) they could remove it.