You may be surprised to learn that it was an all-Polish squadron that scoured the most enemy kills and fewest lost planes during the Battle of Britain. These Polish pilots reported enemy kills only when doubly-confirmed. This careful reporting was meant to accurately display their value to the doubting British military and public. Author Kenneth Koskodan accomplishes a similar goal with the same means. Based on first-person interviews, official military documents, and other published works his well-assembled account dispels any doubt one may have about the Poles' important contribution to the Allied war-effort.
In No Greater Ally: The Untold Story of Poland's Forces in World War II Koskodan aims to correct the errors and ignorance which traditionally surround the Polish military forces in the war. In-depth English-language histories have been absent, and until recently Soviet oppression had prevented the Polish themselves from freely writing about their part in the war. The author's writing is enthusiastic, while keeping the objectivity of a proper historian.
The German invasion of 1939 did not proceed without a serious and determined challenge from the Poles. That old story of a pathetic Polish cavalry charge against German tanks is revealed to be a myth of fascist newspapers. Much like highly mobile dragoons, the Polish "cavalry" actually dismounted to attack with effective personal anti-tank weapons. Koskodan addresses other long-held distortions and brings the obscured accomplishments of the Polish forces to our attention.
No Greater Ally tells of the Polish military forces' dramatic escape from the German and Russian invaders, their attempt to support the poorly-lead French, their highly successful role within the British army and air force, and the ill-fated resistance of their secret army in Poland. Polish fighting skill, zeal, and success impressed the Allies. Yet, the war-weary British and Americans abandoned the Poles to subjugation by the Soviets in 1945. The Polish heroism and the devastation brought to their country will impress any scholar of World War II.
P.S. Polish forces fought with the Allies all across Europe and North Africa. This book is a broad overview of Polish military service during the war. If you are interested in details particular to a certain battle then you'll need to find a more specialized book.