Neither the United States nor the United Kingdom recognized the Polish government-in-exile in any official way although the American government did show a little interest in the organization. In 1948, after Stanislaw Mikolajczyk, who had been prime minister of the government-in-exile during the war, fled from Poland after the Communists rigged elections against him, the State Department recommended to him that the reunite with the government-in-exile in London. As one ranking member of the State Department put it, however, the United States had "no definite plans" to work with the government-in-exile, nor was it "particularly interested in the form which such collaboration may take" between Mikolajczyk and the government-in-exile, although "it was not inconceivable" that such a union of Polish exiles could "at some future date prove very useful." And while it was not inconceivable, it never came to pass. Instead of utilizing the barely-functioning government-in-exile (which, humorously I think, broke into factions despite not having any real functions to perform), the United States instead worked with the Communist government of Poland to try to build bridges with the people of Poland, for example by extending Most Favored Nation trade status to Poland.

In the first years after the war, the United Kingdom actually protested what little support the United States did extend to the government-in-exile. In particular, when the United States suggested that Mikolajcyk should reunite with the government-in-exile in London, the British Foreign Office said that such a reunion would complicate the assimilation of displaced Poles and could possibly hurt British relations with the actual government in Poland. Nothing ever came of this American suggestion anyway and I'm unfamiliar with any other communications that Britain had with the United States regarding the government-in-exile in London.