According to this article, which is an extract from the book Falcon by Helen MacDonald, both the British and the Germans trained Peregrine Falcons to intercept messenger pigeons during the Second World War. There was even a British anti-pigeon force. MacDonald says that the inspiration for the anti-pigeon falcon brigade during WWII came from stories about trained falcon being used in the Franco-Prussian War in the 1870s. See here for the pages in the book that talk about this.