In the US, it's they're immigrsants, we have no idea who they are, half of them are probably terrorists, BS of course but that's how a certain section push it
In the long run it probably is in Labour's interest, they'd likely be in power much more frequently becausethe hard left, which has always been their achilles heel, will be nullified to a certain extent, they same would pronbably apply to the Tories and their hard right side, so essentially there'd be more centrist policies overall, but you're right, in the short term it would probably cost them