Frank Field used The World At One (on which Martha Kearney yet again demonstrated her political illiteracy - can you guess how?) to call for a "double lock" on immigration, preventing those from outside the EU who take a job in the United Kingdom from staying once they have left that job, coupled with a cap. He said that Labour backed the former and the Conservatives backed the latter, but that both were needed.
He is right, and if you want there to be at least one more MP who agrees with him, then please avail yourself of the PayPal button on this blog. But with one caveat, to which I suspect that he would assent: Her Majesty's subjects from her other Realms and Territories, and from the very few countries (all of them small) that retain some other constitutional tie, should have at least the same rights of entry to and residence in the United Kingdom as are enjoyed by EU nationals.
Of course, there would be no problem of illegal immigrants undercutting legal workers on blue-collar sites if you still needed a union card in order to work there.