The UK is not subordinate to the US. The US does not direct UK policy.
Absolutely adorable that you think this. US has very direct impact on UK policy and UK politics, and being part of US run NATO is the main reason UK is deeply involved in the war in Ukraine right now.
No, it doesn’t. The UK has its own military, and it’s own military-industrial complex. The UK is not at war. It’s in a co-operative military alliance, so if someone like Russia came to invade, the US would assist.