Yes, you have a “plastic economy” Polish hat eagle badge made by Alfred Stanley & Sons Ltd of Walsall, one of the more prolific makers of the plastic WW2 era badges. In fact, it was this maker that first proposed the use of plastic (more accurately cellulose acetate) for badges early in the war in order to save metal stocks desperately needed to fight the war.
These plastic badges were not very popular with the Poles, and often when the opportunity arose they were disposed of in favour of metal or even bullion thread equivalents. This combined with the instability of this early type of plastic and its brittle nature now means these plastic eagles are scarce.
Pictured below is Piotr Wybraniec of the Polish 1st Independent Parachute Brigade with one of these plastic eagles on his beret.