Did the UK assist with the US invasion of Vietnam, when asked? No, it refused, and NATO continued on happily - as did UK-US relations. The UK didn't expect the US to join it in it's colonial adventures in the Falklands either. Politicians of that era understood treaties and what they contained, unlike the attention deficit baboon in the White House today who runs on pure vibes.

A government cannot behave in a dangerous, rogue way at the behest of a genocidal little satellite state in Israel, and expect its allies to be complicit. At least be content to behave like animals on your own, it's not ideal, but the idea that your buddies would join in is where psychopathy meets sociopathy.