Plus, and I could be wrong, I thought the UN usurped the UK through the General, rather than the US taking over alone.
Nope. The UN and UNIT pretty much stayed out of it, providing support staff to whoever was in charge.
You might recall that at the beginning of "Day Five," Home Secretary Denise Riley is briefing Prime Minister Brian Green on the British Army's child abduction operation in the briefing room. United States Army General Pierce is in the room and demands that the Home Secretary brief him on the British Army's operation and cease briefing the Prime Minister.
HOME SECRETARY RILEY (to the Prime Minister)
We've isolated 2,600 primary schools, sir.
GENERAL PIERCE
I'm sorry, but you'll address me in all matters concerning this operation.
HOME SECRETARY RILEY
This information is for Mister Green.
GENERAL PIERCE
You and Mister Green -- and this government -- have proven yourselves incapable of handling this crisis. All decisions will now go through me. You were saying?
HOME SECRETARY RILEY (looks to the Prime Minister, who does not look to her; hesitates; to General Pierce)
We have 2,600 primary schools listed here. We are mobilizing transport. At 1200 hours, the British Army will take the children from their schools to the designated rendezvous points.
PRIME MINISTER GREEN
What if they refuse, the soldiers? We could have a mutiny on our hands.
GENERAL PIERCE
They've been told: Any soldier refusing to do his duty will make his own family liable.
HOME SECRETARY RILEY
So we take them to the rendezvous points. But what then?
GENERAL PIERCE
We're about to find out. They're [UNIT] entering Thames House right now.
Basically, the United States Armed Forces, with nary a word of protest from the Prime Minister, overthrew the British government and assumed control of the British Army -- and, therefore, the entire United Kingdom -- for the duration of the crisis, purely on force of personality... and presumably on implicit threat of violence if the British government refused.
It was the UNIT General who was entering Thames House; Pierce was the US Military Representative, not with UNIT.