Can I claim back tax on unused fuel on fuel card

Hi, I am again deciding whether to take a company car or opt out and take a car allowance. If I take the company car I also get a fuel card but the BiK for this fuel card is horrendous (£5600) more than the actual BIK for the car! I have worked out I would need to do 20000 miles just to break even and I typically do 12000 miles a year, roughly 3000 of which are personal. I am in construction and I am wondering is there a way I can take the company car option with the fuel card and claim back tax I have paid on fuel I have not used in previous year? Because my company has fuel cards all mileage is logged so should have all figures too hand. I wouldn't mind paying for the fuel if I was anywhere near using the full amount. Is there any way of reducing the fuel tax side of the BIK.
Any suggestions welcome.

P