But those examples are exactly the point being made (possibly except Brown and Obama), they aren't cooperation, they are supplication, UK leaders following US lead in the hope of gaining good favour. That's not a "special relationship", it's being a lapdog and public support was low throughout.
The British leaders I mentioned seemed to be trying to enact similar domestic policies as their American counterparts at the same times and not in order to impress the U.S. counterparts but due to having similar principles and preferences/ideology.
Regardless, yes joining on military interventions probably has contributed to a lot of alienation and desire to not have a lot of closeness and more following.