In a word: politics. Governments-in-exile were desperate to maintain their own armed forces (albeit equipped by and operating under the direction of another country) as a means of gaining political influence, a reason to be involved in military and political decisions about the direction of the war, and territorial questions after it.

Looking at the Royal Air Force, in 1939 around 5,000 Polish air personnel had escaped to France after the German invasion. The RAF and French air force each agreed to form four Polish-manned squadrons, though neither were particularly keen on the idea and procrastinated in actually putting the agreement into practice. When the Poles started to arrive in Britain they were enrolled or commissioned in the RAF Volunteer Reserve (RAFVR), thus part of the RAF, despite the objections of Polish politicians. The fall of France somewhat changed the situation and in August 1940 more formal agreements were drawn up including an Anglo-Polish Military Agreement and the Allied Forces Act 1940 that allowed allies to raise and maintain their own armed forces in Britain. Polish personnel were released from the RAFVR and then served in the Polish Air Force, though entirely under the operational control of the RAF.

For the general relationship between Britain and Poland see Britain and Poland, 1939-1943, Anita Prazmowska; for the RAF specifically see Flying for Freedom: The Allied Air Forces in the RAF 1939-1945, Alan Brown, which also covers the Czechoslovakian, Free French, Norwegian, Belgian and Dutch squadrons.