While I'd like that to be an accurate description of why the Tory party lost, my understanding is that the migration topic was basically the only thing the Tories did that continued to resonate with voters, and what actually lost them was a continuing series of incompetent leaders, starting with Cameron (who didn't realise the mic was still hot immediately after resigning). Nobody (of any party) liked May, Johnson got away with pleasing lies until Partygate, Truss was a forgettable joke, and Sunak was basically Jim Hacker.

IMO the only reason the Tories didn't lose sooner was that the Labour party was also stuck with Corbyn.