I reckon the tax code situation helps your case and may be the clincher (others may not agree - please comment).
If it was a company-owned vehicle provided for your personal use (as well as business use), your P11D entries each year will show the taxable value as defined by HMRC, and this either reduces your tax code or results in a 'taxable pay' entry when HMRC assess your annual liability under PAYE. It will occur each year since 2006.
If your employer gave you the car, it would have had to declare a one-off taxable payment to you in the financial year 2006-7, of the total capital value of the car - and this would have been shown in your P11D for that year alone.
Assuming the latter scenario, you could be home and dry - but does the second scenario apply?
If it wasn't I don't see how you can claim you own the car under the above idea - and indeed if you've been paying tax on the assessed value (the first scenario), you will still have a tax liability if you are eventually successful in your ownership claim.