Maybe you can explain to me how leaving the EU will assist in preventing illegal immigrants from entering the country.

Everything I've heard from the 'Stay' campaign suggests that leaving the EU will make it far more difficult, especially in respect of the Calais/Dover crossing, to enforce border control as well as meaning that the Eire/Northern Ireland border will have to be made secure as well as potentially the Scottish/England border which will stretch resources even moreso than they currently are.