I think that it may be just a little more complex than that, Vlad.
May has impaled herself on the cross of Brexit. My judgement is that "Brexit means Brexit" had nothing to do with leaving the EU - that stuff could come later - but with making the Tory party a home-from-home for UKIPpers. (In other words providing a substantial semi-permanent electoral majority.)
Since UKIP's main gripe appeared to be all those bloody foreigners blocking up hospitals, swamping schools and claiming endless benefits, May has to be seen to be doing something about them. I suspect that she believed that since the average UKIPper's brain contains only three working neurones, anybody seen being thrown out of the country would gladden his or her heart.
She picked the wrong victims.