Sort of to both, but not really.
Slavery has existed for at least as long as states and kingdoms have, yes. But the specific form slavery took in the Americas (not just the US and North America) was unique. That being race-based chattel slavery. That form had not existed anywhere else in the world previously or since. The closest you could claim were the Helots in ancient Sparta, but even that was closer to serfdom than chattel slavery.
So, no, the British did not "invent slavery", but they (along with the Spanish and French) did pioneer a new form of slavery that was uniquely brutal and inhumane.
And while you're correct that America as a nation did not adopt slavery from the British after the formation of the US since the colonials had already been practicing race-based chattel slavery before the US existed. But where did those colonials get that slavery? From the British who were their overlords and ancestors, who formed the colonies, and who created the economic system that relied on race-based chattel slavery.
So while you might be technically right, it's only due to semantics. The Brits absolutely did create virtually everything about the American system of slavery, which we then continued to perpetrate for another ~century after independence.
Fun fact: Monopoly was originally called "The Landlord's Game" when it was created and was meant to teach people about the fundamental absurdity and contradictions inherent in the capitalist system of land ownership. It was later co-opted by a family member of the creator who sold it to Parker Brothers. They renamed it Monopoly and turned it into the commercial success it is today.