We have drone images with WGS84 positions, what do you mean by this?
“When you’re using Lat/Lon coordinates, you need to use WGS84 coordinate system, not the same as for meter’s values.”
You used both coordinate systems in your import settings. The file name is called WGS, but the selected CS was set to OSGB36:
The best option is to have the seme project and output CS. So, for your case 27700 - OSGB36
Couldn’t we remove the unsupported coordinate systems from the list?
Sometimes there is an option to use also the geoid’s heights: How to improve a registration - #11 by OndrejTrhan and the file with ESPG codes is from external source, so basically all available are there.