If UK leaves can Ireland keep the free access to UK? Well, should be No, but see the Norway situation with EU Scandics. But NOR is member of the EEA and of Schengen.
But if UK is part of EEA then it will still have to let Greeks, Poles, Spaniards et al work in the UK! Are Cameron (and even Miliband after his recent apologies and other views re intra-EU migration) aware of that?