I'm sure someone like Al-R will correct me, but you can only claim for mileage actually driven (in other words, expenditure that you have had to make in relation to earning a salary). When I was travelling very widely with a previous appointment, we lived off-base so I used my own car to travel direct to locations. I could claim for this mileage (discounted by payments made by the RAF) but not for normal commuting mileage, ie from home to my office.
I enquired with the Tax Help Line (who were particularly helpful, I might add) when I was posted to London about the additional cost of commuting Mondays - Fridays some 300 miles each way, albeit by train. When the sums were added up - train ticket costs, bus fares etc - it worked out roughly cost-neutral, but Inland Revennue (as was) did query the cost-free accommodation in London and basically implied that I would be kicking the arse out of the system if I attempted to claimfor the additional mileage!
WP