bit late Royalist.... think back to B-29's, Polaris, Trident etc etc
our armed forces are all very very closely integrated with the US and have been for years
We cross-post staff, we have Brits involved in long-term planning at RAND, we used to test our N weapons near Las Vegas. The US runs acres of the UK as "RAF XX" bases and also effectily owns Ascension and Diego Garcia.
TBH we're almost as close (and a lot more tractable) than the US Marine Corps to the US military effort