“Rights of Englishmen” and “natural rights” are two different categories.
The right of Protestant subjects to keep and bear arms was indeed a historic English right. You can find it in the English Bill of Rights (1689).
There’s very little record in Veit, et al.’s collection of the original documents regarding Congress’s proposal of twelve amendments to the states in 1789 relating to the 2nd Amendment. I’m not aware of any state’s ratification convention saying that it wanted a guarantee of the right to keep and bear arms in order to keep slaves down. Federalists had said during the campaign over ratification of the unamended Constitution that one reason people needn’t fear giving Congress power to raise an army was that every American man had a gun, and so the federal army would never be able to overpower the militias. One infers the 2nd Amendment grew out of this argument.
Of course, the English provision was not about suppressing slave uprisings, as there were no slaves in England in 1689. This whole concept seems a bit fanciful, not to say tendentious.