Other than sharing a similarly-principled operating system and the same designer, no, the 1911 and BHP are two distinct, separate and fairly distinct designs, and were originally designed for two different chamberings (.45 ACP versus 9x19mm), and initially commissioned by the militaries of two separate nations (the USA versus the UK). The 1911 continues to have a strong following and practical user base, while the BHP despite being an OK design and having a distinguished service history has become almost completely abandoned for all practical purposes. The BHP's (actual) design shortcomings such as having a magazine safety--exacerbated in the hands of the fictional arrogant sheriff--were the butt of literary criticism in the original novel "Rambo" (which was the basis for the movie, but differed in presentation of details).