Conservative shadow foreign secretary Priti Patel has flown to Washington to attend a Republican-hosted event at the inauguration.
Speaking to the BBC she said there were “hopes for his [Trump’s] administration”.
“We need to continue to build upon that and at a time when our world is facing so many global challenges… we need to ensure that our strongest and closest ally is really in lock step with us,” she said, adding that meant reopening trade deal discussions.
Reform UK leader Nigel Farage said the government needs to “think outside the box” when dealing with the Trump administration.
Speaking to BBC Radio 4’s The Westminster Hour, Farage said: “I think what this government does, is what all governments do – they stick with the established, status quo methods of appointing people.
“This guy [Trump] does business differently to anybody else we’ve seen in global politics before.”
Farage, a long-time supporter of Trump, has previously offered to act as a go-between in negotiations with the president-elect but has so far been rejected by the government.
“They don’t think they need me – but they might find in short order that maybe they do,” he said.
Elsewhere, Liberal Democrats leader Sir Ed Davey said that Trump’s return to the White House would be “deeply worrying for millions of people in the UK and around the world.”
He said: “With a president who promises trade wars, undermines Nato and praises Vladimir Putin, the threats to our national security and our economy are clear.”
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