Britain's new prime minister faces the dual challenge of reviving a post-Brexit relationship with the European Union that has made little meaningful progress, while also managing renewed friction with the United States under Donald Trump. The incoming leader has signalled a preference for focusing on domestic priorities over foreign policy, raising questions about how aggressively the government will pursue closer ties with Brussels. The situation underscores the difficult balancing act facing London as it navigates relationships with its two most consequential international partners simultaneously.