What, the "we're full" argument? Really, when there's 1 immigrant every 10 square miles.
Why not build more housing, it would help reinvigorate the economy and if more immigrants arrive and work here happily paying their taxes then their contribution will help pay for our increasingly ageing population as well as our idle minority who don't want the work.
The reason the remain campaign have probably not raised the immigration argument is that they realise that neither side has the answer to it, in fact they know it's not really a problem anyway. Of our immigrants only 1 in 10 illegal immigrants smuggle their way into Britain, most arrive legally and then overstay their visas so taking back our borders (which we never actually gave up) will achieve very little. If anything seeing how well most of our civil service works we'll probably allow more through than get through at present. We try to tackle the black market employers who keep illegal immigrants in usury and modern slavery, the traffickers who bring them over etc but successive governments have failed to put a significant dent in the numbers because our incessant need for cheaper services and goods creates the market conditions that bring them here in the first place. The legal economic migrants from the EU and elsewhere actively contribute to our society and are a net benefit to the countries purse despite many of them living in pretty horrendous conditions and doing work our own labour force will not, even if we leave the EU we will still need similar numbers of willing workers prepared to accept low wages and poor conditions, I'd love it if all workers were well paid and well treated but capitalism put paid to that dream decades ago.
The simple fact is, immigration is not actually a problem so no government is going to go to great lengths to try and tackle it other than staging a few high profile raids in support of the modern day slavery bill. That won't stop the politicians using immigration as a convenient smoke screen for everything else that ails us, it's always been easier to blame our woes on Johnny Foreigner than to tackle the real issues and frankly our ruling class would rather their mates in big business are left in peace to dodge tax and exploit the poor whilst we're busy buying into the press manipulation that demonises the immigrant, the poor, the sick and the needy.