At least the regular American workers and GIs stationed in the U.K. don’t be have diplomatic immunity.
Even during WW2 they weren't subject to UK law. If they committed an offence it had to be dealt with by the US military.
I thought it was a well known fact that the US doesn't recognise foreign legal systems as a starting point ? Which is why it seems a little bit odd to want to jump into bed with them.
Although to balance things, the UK has refused to extradite a few people to the US in the past. But not under the cloak of diplomatic immunity.
I wonder if anyone remembers the parade of Libyan diplomats leaving the UK after the murder of Yvonne Fletcher ? So that's two countries we can group together: the US and Libya under Gaddafi. I wonder what other similarities we can find ?