Five years after it left the European Union, Britain may have finally found a new role on the global stage — a gig that looks curiously like its old one.

In the frantic few weeks since President Trump upended the trans-Atlantic alliance with his overtures to Russia and rift with Ukraine, Britain’s prime minister, Keir Starmer, has tried to act as a bridge between Europe and the United States.

Mr. Starmer and his top aides counseled President Volodymyr Zelensky of Ukraine in phone calls and face-to-face meetings about how to mend fences with Mr. Trump after their rancorous White House meeting. The prime minister has energetically lobbied the American president for security guarantees to deter President Vladimir V. Putin of Russia from future aggression.

In his high-wire diplomacy, Mr. Starmer is reviving a role Britain routinely played before Brexit. He bears comparison to Tony Blair, a previous Labour prime minister, who tried to mediate between President George W. Bush and European leaders in the fraught lead-up to the Iraq War in 2003.

Mr. Blair’s bridge-building didn’t end well, of course: France and Germany refused to join Mr. Bush’s “coalition of the willing” against Iraq, and Britain’s lock-step alignment with the United States frayed its relations with its European neighbors.