if you use a privately owned vehicle for business travel you can claim per mile from your employer at 45p/25p per mile. That's not for fuel - it's for everything: depreciation, insurance, maintenance, tax (and fuel) etc. it applies irrespective of how your car is fuelled.
The only minor spanner in the works is VAT reclaim from the company perspective.
Some employers like VAT receipts for the fuel portion (i.e. up to the approved company car rates, as it means they can reclaim VAT on the fuel portion.) I have heard of some people getting their claims bounced by overly strict requirements of the accounting department without fuel receipts covering this amount of VAT.
This only makes it a timing issue though, as you can reclaim it at self assessment time from HMRC (as dpeilow suggests)