BGT is a TV show and acts can't have control over a TV performance, as there are legal issues in getting the rights to the songs, etc. especially if you want to change/modify it a substantial amount. Add into that dealing with the rights of the songs used on ITV player, YouTube videos, etc and it can get quite messy, hence why BGT/XF often use the same songs from Sony's back catalog that they have all the rights too.



