Theresa May's team believe her meeting with Donald Trump went "as well as it possibly could have done", ITV News Political Editor Robert Peston told News At Ten.
He said there were signs of the "beginning of a good relationship" but "the hard work starts now".
Meanwhile, ITV News Washington Correspondent Robert Moore said that the president had delivered a "measured and disciplined" performance and that the day had been a "victory of sorts" for those hoping Mr Trump will become more of a "conventional" figure than he was on the campaign trail.
Watch the full analysis by our correspondents:
To be clear, this was as benign and accident-free a start to a new "special" relationship as Theresa May and her advisers could have wanted.
Voice and body language expert Caroline Goyder writes for ITV News about the signals given off during the meeting between the two leaders.
In the past, Mr Trump has described the organisation as "obsolete" and questioned the contribution of some members.