Theresa May has been urged to learn from French President Emmanuel Macron in her approach to dealing with Donald Trump.
Former foreign secretary Lord Hague said the UK's approach to the transatlantic relationship was to be "solid but not slavish", adding that under Mr Trump there were now "many more subjects on which to be 'not slavish'".
The ex-Tory leader said Mr Macron had shown it was possible to have a constructive approach to dealing with the US president.
Lord Hague told peers on the International Relations Committee that the divergence between the US and Europe on foreign policy was "probably a trend not a blip, unfortunately".
Mr Trump had done things "probably most or all of us in this room would disapprove of" such as withdrawing from the Paris climate deal and moving the US embassy in Israel to Jerusalem, he said.
On the relationship with European partners, Mr Trump "is less polite" than Barack Obama about the need of Nato allies to pay more but the message was broadly similar, Lord Hague said.
But overall Mr Trump was "accelerating rather than inventing some of the changes in American foreign policy" including the focus on Asia which had begun under Mr Obama.
"How to handle this is a very important consideration for the UK," he continued.
"In a tactical sense I think President Macron is giving a very good display of how to handle these things and how to have a relationship that is frank but close at the same time.
"I hope that is how the UK Government can operate.
"My phrase as foreign secretary was to be solid but not slavish with the United States, but there are now many more subjects on which to be 'not slavish'.
"I don't think that need be fundamentally damaging to an overall alliance with the United States."
Mr Trump was invited to make a state visit to the UK by the Prime Minister in January 2017 but is not expected to actually come to the country until the second half of 2018.
He has already been to France, where he was treated to a grand military parade, and Mr Macron will travel to the US for a full state visit this year.