The thing about the United States is that after you achieved independence, some of the great men who lead your nation at that time, decided that they needed to restate some of the principles of Common Law, and incorporated them into the Bill of Rights.
And in restating them, they went further than the Common Law did on a couple of issues, including on the right to bear arms.
The implementation of that law in England, and subsequently in Britain, and then in the Empire, was more limited by the text of the Bill of Rights of 1689:
That the subjects which are Protestants may have arms for their defence suitable to their conditions and as allowed by law;
The religion bit is irrelevant now - but those last five words make a lot of difference. It allows laws to be made that restrict the right to bear arms without violating the Common Law.
As in the UK and now Australia, right?