"Road_Hog®" <No Spam> declared for all the world to hear...
> What legislation licences you to change the IMEI in the UK?

Section 1, paragraph 3b of the Act you quote in another post seems to
fit the bill.

Also explained in the explanatory note paragraph 5.

> Besides, we're talking about reparing/rewriting the IMEI to a phone.

You are still changing it.
--
Regards
Jon