[sometime lurker]

You are wrong. Blackstone's commentaries are considered authoritative, and he says otherwise. You are quoting something brought up in the House of Commons in 1604. A little more digging would show you that it never became law.

in 1604 Commons debated a measure to pin down the status of English born progeny of aliens, granting those "of 'the first birth or descent only,' and born within the realm the limited position of a denizen." The House rejected the bill on its third reading.

[Mr Rogers]

Thank you.

[Rides3]

You are wrong.

Sorry, I'm not wrong.

Three other sources:
Charles Viner's Abridgment of Law. 1741 and 1756
Timothy Cunningham's Law Dictionary. 1764 and 1783
Giles Jacob's New Law Dictionary. 1729, 1762, 1772, and 1782

I'll save you time and trouble... all three reiterate the English law declaring that English-born children of alien parents were denizens, NOT natural born subjects.