""my firm say that if i paid tax i would b able to claim it back at the end of the tz yr""
This sounds as though you might be self employed - if you were on PAYE, you should be able to get it back through your tax code.
It's only Self Assessment (self employment) where you claim at the end of the tax year.
I don't see that paying tax is anything to do with an employer paying mileage.
There are Mileage allowances which the Taxman approves - about 40p per mile for the first 10,000 miles - but the decision whether or not to pay mileage is up to the employer.
It appears you may not be getting a proper story from this firm, but if you kick up a fuss, you,ll probably be looking for a new job...