The criticisms of Starmer's language around migration are just nonsense in my opinion, I haven't seen any convincing piece yet to justify it.
Putting that aside, I don't think the policies will win votes unless they work, the public were lied to about migration for years (X target, then X target again, then Brexit will reduce it). The sad truth about the British public is that if Starmer reduces migration substantially, there's a good chance he wins the next election. He could make no progress elsewhere and it wouldn't matter to a lot of people.
I don't tend to ask people how they have voted so wouldn't know if any have switched.