I think you're attacking a straw man here. Chinese and Indian people can certainly compete with European people, and they do it everyday. But they can do it from China and India.
When really, they got out competed in trade and on the battlefield by the Europeans.
So it's equally as fair for those laborers (voters) to say "no more importing cheap competition". The UK already has. It's incredibly difficult to bring in foreign employees.
Edit, addendum, ignore the part about companies, though you'd said European firms.