I can only go by what the news tells me but they seem to suggest that the increase is real. I don't know how the public can check that. (It's possibly overstated tin order to sell papers or attract advertisers.)
But obviously the racists in society would not be wanting to support 'remain' with it's policy of let everyone from the EU just walk in here (and I stress that just because folk with a metal quirk again other races/nationalities would be 'leave' supporters, the reverse is clearly not true) and now 'leave' having won the referendum they may be emboldened enough to make noise and harass folk they don't approve of.
Ultimately the solution is to make it clear that, that was unacceptable prior to the vote, it is still unacceptable today, and will continue to be so.
To be honest decent folk will already indicate this to them, but the media highlighting it may well encourage such activity. It's the authorities that need to consider how to respond to clamp down on it. If they aren't too busy changing their leaders.