There has been many a Masters and Doctoral thesis written on this. British common law dealt with subjects, property of a state and their relationship with that states monarch or king/queen. The US constitution deals with the relationship between free men without any King who we where throwing under a bus at gun point at that time. The only commonality of British common law and US law is both are written in English. The founding fathers pointedly did not use British common law in writing the Constitution.
With all due respect, that is simply not accurate. We have evolved from it over the course of the years and enacted statutes to change things or to expand things, but the English common law remains the underlying base - and if there has been no statute to specifically provide guidance in a dispute, that is what will likely rule the day entirely.