I’m curious why the OP allowed 6 faces. Although he’s entitled to make whatever rules he wants, and to decide just how close an analog to Mt. Rushmore he has in mind.
The faces on Mt. Rushmore are all presidents, holders of the highest office in the land (which in the UK would be monarchs? prime ministers?); and a case could at least be made that they are the greatest of our presidents and did the most to make the nation what it is/was at the time the sculpture was designed, and/or that they stand for four phases of the nation’s development: its birth, its growth/expansion, its preservation through its greatest crisis, and its looking beyond its own borders to become part of the international community. Are there 4 (or 6, or however many) UK leaders who hold similar status?
Alternatively, if you were gonna do a “Mt. Rushmore” for the UK, you could pick a face to represent each of England, Scotland, Wales, and Northern Ireland.