Guidance note 8 (earthing) from the IET is worth looking at if you borrow one, I would not buy one at the moment because it hasnt been reprinted for the 17th.As far as exporting an earth as you rightly say no problem with TT, the more paths to earth the better
If the swa to the garage has no earth protection at the moment then it must be brought up to date with either its own RCD or RCBO as it is a seperate circuit
Now as soon as you alter or add something you become responsible for the whole gambit which means as someone already said poor access to the house DB is not acceptable, when you sign the installation cert you sign for all your work or anything you have added to or altered being up to the current regs which includes access