Three Labour MPs and two Conservatives voted unsuccessfully for the recommendation to be dropped but were over-ruled.
The committee said that the relationship was more associated now with the perceived support Britain gave to President George W Bush over the Iraq war.
“The perception that the British government was a subservient ‘poodle’ to the US administration leading up to the period of the invasion of Iraq and its aftermath is widespread both among the British public and overseas,” it said.
“This perception, whatever its relation to reality, is deeply damaging to the reputation and interests of the UK.”
The committee also said US President Barack Obama had taken the same “pragmatic” attitude as it was recommending now since entering the White House in 2009.
It said: “The UK needs to be less deferential and more willing to say no to the US on those issues where the two countries’ interests and values diverge.
“The UK’s relationship should be principally driven by the UK’s national interests within individual policy areas. It needs to be characterised by a hard-headed political approach to the relationship and a realistic sense of the UK’s limits.”
Heck of a job W.