It is interesting, cos the right has colluded with the (mainly) tabloid press in particular to foment this anti-immigration feeling in people, but it's potentially backfired on them in terms of their economic interests. May, like Cameron, was opposed to the Brexit, presumably on the grounds of it being anti-globalisation/free trade, and the British population gave them the message (on the whole) that 'we don't want globalisation/free trade/immigration'.
There's something similar going on in the US with the Fox news network whipping up all this anti-immigration stuff and giving birth to Trump, who has steamrollered all over the Republican establishment.