For at least 40 years, since long before the changes wrought by the Blair Government, it has been a question of national sovereignty or the House of Lords, "but you can't have both."
That that House would certainly block withdrawal from what Tony Benn always understood and said was really the EU, was his principal reason for wanting to abolish it.
The Conservative Party could not find a thousand new pro-Brexit Peers, and in any case it would not want to.
This whole matter is about to come to a head. Not before time.