Well, I was confused at the start of the Traveling Geeks tour, but have learned a coupla things. This is my (over-simplified) version.
The "government" in the UK is the majority party, who selects ministers including the Prime Minister. It's somewhat analagous to "administration" in the US. (The majority might be a coalition.)
There's no formal transition period in the UK, and far fewer political appointees.
The opposition party maintains as "shadow cabinet" which is ready to replace the existing cabinet immediately.
Feedback appreciated, I'd really like to get this right.