SASLess, I did draft a longer response but it vaporised.
Why there? because the Vietnam war was just an extension of all the other Asian conflicts post 1942. The Dutch in the East Indies, Korea, the communists in Malaya, Indonesians in Malaysia, the Taiwan issue and so on. SEATO was the 3rd treaty in an attempt to contain the spread of communism and it is probable that communism spread on the basis of my enemies enemy is my friend.
The area was divided between UK and US with the dividing line at 105 deg East (I am not forgetting the active participation by ANZAC forces). Some of our targets were in the north of Vietnam practically on that 105 deg boundary.