A380
I do not see what the problem with an A380 is.
The official charts for BHX have Airbus 380 approved taxiways marked on them, it fits on the stand which I believe is marked and the terminal can cope with the passengers. It fits better than the Wardair 747 on the old terminal with the 707 steps and the Herald steps welded onto the top. It is a good job that Health and Safety did not exist in those days.