Enemies at home and abroad

If the UK had entered the Vietnam War after the Labour victory of 1964 could popular culture provide a strong anti-war voice in much the same vein as the Smothers Brothers:

For example IOTL the 1970's Dr Who stories had a political twinge. Could the Troughton/Pertwee/Baker 1 period have a similar effect on UK opinion?

(NB there was a YT channel called Troughton Lover which contained an excellent documentary called "When Worlds Collide" but it has been taken down which is a real shame)
 
Maybe the combined US-UK forces could have brought an earlier end to the war, say around 1967, so the anti-war movements that came in 1968 (and spread) would not happen.
 
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