When David Cameron, Britain’s foreign secretary and onetime prime minister, visited Washington last month, he took time out to press the case for backing Ukraine with Representative Marjorie Taylor Greene, the far-right Georgia Republican who stridently opposes further American military aid to the country.

Last week, Boris Johnson, another former prime minister, argued that the re-election of Donald J. Trump to the White House would not be such a bad thing, so long as Mr. Trump comes around on helping Ukraine. “I simply cannot believe that Trump will ditch the Ukrainians,” Mr. Johnson wrote in a Daily Mail column that read like a personal appeal to the candidate.

If the “special relationship” between Britain and the United States has taken on an air of special pleading in recent weeks, it is because Britain, rock solid in its support for Ukraine, now views its role as bucking up an ally for whom aid to the embattled country has become a political obstacle course.

British diplomats said Mr. Cameron and other senior officials had made it a priority to reach out to Republicans who were hostile to further aid. For reasons of history and geography, Britain recognized that support is not as “instinctive” for Americans as it for the British, according to a senior diplomat, who spoke on condition of anonymity because of the diplomatic sensitivity of the matter.