Irish players are fine, NI is still in the UK and the Republic has an agreement with the UK predating the EU whereby we are allowed free travel within the UK (I believe)
http://www.citizensinformation.ie/en...nd_the_uk.html
I'm pretty sure the organisations (ECB for cricket, FA for football) can either a) sort out visas for players or b) work out some agreement with the UK government to loosen restrictions on professional sportsmen or some such rule.