No, the UK embraced that idea before the US did (many of the specific rights and the legal language used to describe them are taken directly from their articulation in British predecessors); the formation of the US was largely a reaction by elites educated in British norms being unhappy that the ideas that were accepted in Britain were applied with less consistency in overseas territories with special legal status.

A practice, one might note, that the US has also continued.

If you would compare the Bill of Rights to the UK system, I'd be interested.

If you leave out the Code of Hammurabi from about 4000 years ago. And the Magna Carta and a few other things.

An eye for an eye, a tooth for a tooth? A written system of laws and punishments, duties and privileges, is not based on principles of inalienable rights of men, equality before the law, etc.

"Research by Victorian historians showed that the original 1215 charter had concerned the medieval relationship between the monarch and the barons, rather than the rights of ordinary people" https://en.wikipedia.org/wiki/Magna_Carta