The Socialist Party seeks the replacement of capitalism by socialism. This will be a world-wide society not based on countries or continents or superpowers. So we are not concerned as to whether capitalism is organised on a national or trans-national basis. The EU is clearly a capitalist construct where the dominant elements of the capitalist class in Europe see an advantage in organising the politics and economy of Europe on a continent-wide basis. The reason the existence of the EU generates political heat is that such an artifice brings no advantages to some elements of the capitalist class within each country, yet they feel they must bear a proportion of the costs, so they oppose it.
Does anyone really believe the day-to-day lives of ordinary people in the UK will be significantly affected by the outcome of the referendum? Of course, as with the ebb and flow of capitalist politics, there will be temporary winners and losers among working people of Britain. Those British workers who live and work or are retired in Europe, gain some minor benefits from British membership of the EU. As against that, other sections of the working class in Britain may benefit from an exit from the Union; those employed in sectors where they are competing with migrants from Europe to sell their labour power. However the basic position of the vast majority of the people in Britain will be unaffected by the manoeuvring of politicians on either side of these campaigns. Ultimately only the transformation of the economic basis of society and the scrapping of national and supra-national based identities can do that.
You won't find Socialist Party members standing on the White Cliffs of Dover alongside the Euro-sceptics waving Union Jacks and chanting “Out, Out, Out”. Socialists are not among those sad insecure individuals who feel their identity threatened by cultural integration and arrival of fellow workers from abroad. In or Out is of no concern to members of the working class. Whatever the outcome of the vote, capitalism will continue. And continue it will until you and a majority like you take the revolutionary step of deciding to abolish capitalism in all its forms and to bring into being a new society.