Short term - nothing really.
But we live in a global economy now. Eventually, with the global economy being so intertwined with every other aspect of global finance, everyone will feel the impact. It seems that our economics are somewhat insulated from the initial indicators. But I don't know of any educated economics expert who doesn't understand and expect what is happening in Europe, Asia and elsewhere to not eventually impact our own national economy.
The only recourse of preventative action is to promote growth within our own employment sectors, which requires legislative policy that can help insulate us from foreign influence. I just read today that the EU plans to levy an additional tax burden upon Apple corporation at the tune of 14 billion dollars (US). While that would perhaps help sustain Ireland's shortfall of corporate tax revenue, what it eventually means is that Apple will relocate to a more tax-friendly region. With the UK having removed themselves from the EU - Apple stands to gain from relocating to the UK, as does the UK, with the jobs and everything else that goes along with it.
There is a very fine line between unnecessary and deliberate tax avoidance and a corporation being bilked out of enormous amounts of money. What many governments fail to understand is that these companies' shareholders expect a reasonable return on investment. Whether one agrees with that isn't necessarily related to the exponential value that the corporation is to the local economies... The EU reserves the right to tax whatever they feel is necessary, but at the same time - the corporations are at liberty to relocate to the regions where their efforts are more lucrative.
You simply cannot cut off your nose to spite your face, but that seems to be the MO of the EU. I wouldn't be surprised to see London (or some other UK locale) be the benefactor of all this. And in hindsight - maybe "Brexit" wasn't such a bad deal after all.
Of course, this all depends on one's personal purview....