Hello millie
I am a bit confused by the section of your post where you say
I currently only pay tax for business mileage and nothing I for personal use
Do you mean you have car benefit only and not fuel benefit.
Normally unless you have a car with a low list price and low CO2 emmissions the fuel benefit ia quite high.
The answer will also depend on how much private mileage you do - the morre private mileage the more you will have to reimburse.
I would check the calculation on the revenue website - i do suspect if you have lowish personal mileage you will be better off reimbusing for private fuel.
Not travel to and from permanent workplace is private mileage
http://www.hmrc.gov.uk/calcs/cars.htm