The 40p - 45p per mile is often quoted by dealerships as a "fair" mileage rate deduction. It is loosely based on the HMRC mileage rate of 45p per mile for people who use their own cars for work and is intended to cover fuel, insurance and tax (all pf the things you've already paid for yourself). It is not suitable as a ballpark fair use deduction when rejecting a used car.

Given that you spent £3450 for the vehicle just a few weeks ago, I think it's unfair that the dealership is demanding to keep almost a third of your cash due to the car being faulty.

I would argue that 25p per mile is a fairer rate. If the dealer refuses, ask if they are a member of any trade organisations that will act as a conciliation or arbitration service. Many trade associations will require the dealership to sign up for a code of practice that they will need to adhere to or face removable from the trade group.