Sure that’s what the business class thinks, but not the average person. Britain would be the last stop, migration travels all the way through Europe to get to Britain, and will only increase if things get worse. Despite the hardships more will keep trying to get through as was the case in the mid 2010s, after Syria and Libya had become destabilized.
If British voters can tell their representatives, especially Tories, that the marginal benefit of allowing Pakistani oligarchs to reside in Britain is not worth the uptick in migration, then it will have an impact. Especially if it risks toppling Sunak’s government. This is not to mention all the other European electorates and governments which would be effected by an increase in migration.
Migration of Pakistanis are probably already increasing, despite the risks.