I doubt it would happen. Any government that allows more immigration is a government that will be un-electable for quite a few years. It only took one broken promise for the Lib-Dems to lose 49 seats in 2015.
Nobody was actively voting for more immigration. They were voting for less immigration from the ‘wrong sort’, so they could have more of their own. (Its hard work stating the bleeding obvious without getting rops) But think of the great Bangladeshi curry cook shortage scandal.