You are certainly able to offset the 12p per mile (up to 10,000 business miles per year) against your tax bill. You are also liable, should you do more than 10,000 miles in a tax year, to the tax on the 3p overpayment for mileage compensation over 10,000 per tax year. Depending on your marginal tax rate you could get 4p per mile reduction in the amount you pay the Inland Revenue under the 10,000 mile threshold / 1p per mile increase in the amount you pay the revenue for miles over 10,000 per tax year
It's up to you if it's worth the pain of claiming for the tax on a few miles.
I used to claim regularly. I was having to fill in a tax return anyway and my employers paid 25p a mile, I drove a lot of miles on their business, so I used to claim back the tax on £2,500 a year... at 40% marginal rate that was worth £833 to me, definitely worth the effort of claiming.
Oh, you should work out your costs per mile on your car. If 28p covers your costs, all is OK (and that's a tricky calculation... fuel / servicing / depreciation / marginal extra cost of depreciation for being high mileage). If it doesn't then you are subsidizing your employer's business at your expense and if your employer is charging your travel costs at > 28p a mile to the customer, they are profiting from wearing out your car. I have been in that position and I got rid of my car... traveled to work by train and made them hire cars if they wanted me to travel for work. That lasted for a few months before they decided I could have a company car ;-)
Oh, don't forget in calculating the marginal cost of the car that to use it for work purposes you must have appropriate insurance. That is insurance that covers use for business, not just commuting to your usual place of work. That's often called 'class 1 business' and if you don't have it you should get it as otherwise you are not covered for driving to customer sites