Wikipedia seems to have removed all mention that he is was allegedly legally allowed to use the HRH Prince Ernst August Guelph in the UK that it used to. Although it is still there in his father's entry. Again with no source.
This interview with his son says that Prinz von Großbritannien und Irland is part of his name on his German passport due to it's incorporation in 1914 but that he was simply known as Ernst Hannover in the UK with zero "he's actually secretly a legal British Prince" or Ernst August Guelph.
https://www.haz.de/Hannover/Aus-der...Hannovers-Prinz-Ernst-August-im-HAZ-Interview
HM also didn't use any name that might imply "Prince of GB and Ireland" in her formal approval of either of EA's marriages.
https://www.thegazette.co.uk/London/issue/48638/page/7956
So I think that it's probably just a courtesy title, even in the UK. It doesn't really matter though since just about everyone/thing accepts the notion of courtesy titles socially.
In Caroline's case she also has her own title from birth that even though it's HSH not HRH is indisputably legal and real.