The trouble is that fear of immigration is based on perception not reality. But the perceptions are 100% real - and very dangerous, as we've discovered. You can't counter these fears and beliefs simply by quoting studies and statistics, especially if people end up retreating into their own group because they feel foolish.
Before the referendum, I was at a seminar run by one of the London universities, comparing this ref with the last one, and one of the depressing conclusions was that the endless feeding of negative immigration stories - by politicians looking for externalities to blame, and by the right wing press - (culminating in one front page a week in the six months leading up to the ref vote!) - has embedded a culture in which many people - regardless of the make up of their local populations - routinely frame their concerns in terms of 'immigration' because they believe that immigration is the main cause of the problems that impact on their lives and those of their children - housing, low wages, zero hour contracts, etc.
I suppose we were defo the 'Metropolitan Liberal Elite' - we all knew what the statistical reality was and I suspect that like me, many participants that day would have struggled to get their heads around the idea of people ignoring hard data - but the signs were there - eg a senior union organiser told us - 'all I ever hear when I campaign is 'immigration, immigration, immigration - we're not getting through - we're talking to ourselves'.
And people like Gove gave them licence to feel entirely comfortable about the validity of beliefs regardless of evidential basis.
I don't know how you counter cultural norms once they have become so deeply embedded - it is a colossal task - perhaps even impossible.