Well my little Pocket Book suggests that 2.4m internal width is the minimum for a single garage assuming the door is offset from the space behind. This gives 200mm passenger side, 1600mm for the car, 600mm minimum space to get out on drivers side. These are absolute minimums and a better space is 200+1700+950 equals 2850mm.
Regarding doors and frames, I guess you know the minimum is 6ft6in for both, but 7ft is better. These acursed things are still imperial sizes.
But none of the above has any impact on BR, and as far as I know there's nothing in BR on sizes of garages - as you say. A garage is a non-habitable space and only parts of BR applies to an attached garage - things like fire protection. But I guess you know that.
Are you sure this isn't a PLANNING permission issue, where they are saying you are going to have to park in the road because up to now you've been able to park in the space adjoining the house and now your garage is too narrow to put a car into. Otherwise, why not just call it a large shed, not a garage.