Over population is less of an immediate concern than the ability to fund welfare, unfortunately, we don't have enough people of working age in work and paying tax to afford all the pensions of those in retirement without migrant workers, not in the current system. However, if we are in the EU, planned tax avoidance rules for companies like Google paying bugger all in Ireland, could mean we don't need such a large take from working people.
What is likely is that we will have roughly similar numbers of migrant workers if there is work available, it will just take more time and money to facilitate their visas, in turn knocking those employers profits on which they pay tax, also the Tory leavers tend to be in favour of low corporate taxation, and is one reason they are keen to get out of the EU now, it really is an oversimplification to think leaving the EU and ending freedom of movement will solve lots of problems, it just shifts issues around a bit, and makes quite a few things worse.
There are certain people we need Doctors and Nurses for example but we don`t train young people in this country for jobs ,teenagers are pretty well non existent in my line of work .Yes its a shame these big companies get away without paying enough tax .You say Tory leavers do you mean MP`s or ordinary people ,there were Labour MP,s who voted to leave as well what would have been their reasons ? unless they thought the EU was undermining workers by dropping wages down .