It was a hectic Monday morning for Peter Mandelson, who was packing up his home before heading to Buckingham Palace for an audience with King Charles III, on the eve of becoming Britain’s ambassador to the United States.

But the stress of leaving London may not compare to what awaits Mr. Mandelson when he lands in Washington on Wednesday. Few British diplomats have taken on a job as fraught with political risk as Mr. Mandelson’s. His first day at the embassy will coincide with President Trump’s 18th day in the Oval Office — and already, some of America’s sturdiest alliances are teetering.

As he packed boxes, Mr. Mandelson was keeping an eye on Mr. Trump’s latest exchanges with Canada and Mexico, after he had imposed — then paused — sweeping tariffs. The European Union looked to be next in his cross hairs. Mr. Trump was gentler about Britain, suggesting to reporters that a deal “could be worked out,” though he claimed its trade balance with the United States was “way out of line.”

“I’m not going to tell the president his business when it comes to trade,” Mr. Mandelson said in an interview, striking a scrupulously diplomatic tone. But he insisted, “We have a balanced trade relationship with the U.S. It’s balanced in goods; it’s balanced in services.”

For Mr. Mandelson, the trick will be to keep Britain out of Mr. Trump’s line of fire — and to do it at a time when Prime Minister Keir Starmer’s left-of-center government is trying to reset its relationship with the E.U., to which Mr. Trump has long been hostile.

Mr. Mandelson has already been denounced by a faction of Trump loyalists, who failed to scuttle his nomination but may have played into his decision to apologize on Fox News last week for deriding Mr. Trump during his first term as a “white nationalist” and a “danger to the world.”