I did watch the video you shared, btw, but I didn't feel his argument was especially persuasive.
With ~45 years or EEC/EC/EU membership to refer to, there were zero examples offered where this ostensible move away from common law had actually manifested, let alone in a negative way.
Actually, I thought his position seemed to be the standard nebulously nostalgic nationalism.
I don't recall common law being a talking point in any of the leave / remain discussions and marketing. Cameron originally couched the question purely around economics -- which unfortunately made the public debate, such as it was, vulnerable to grossly influential outright lies around money. The famous '£350m a week’ lie, f.e.
This then seemed to morph (or was manufactured) into some kind of national identity existential crisis.
They're not mutually exclusive.
> I wonder if he'd lived, he'd have changed his opinion
He did appear to be making his decision based on principle, not process, so I doubt it.