Well, hopefully things will be different post Brexit. people who come here should be vetted and working (or at least be able to support themselves.
Yes, and that's what the EU says too.
Migrant workers’ right to reside for more than three months remains subject to certain conditions, which vary depending on the citizen’s status: for EU citizens who are not workers or self-employed, the right of residence depends on their having sufficient resources not to become a burden on the host Member State’s social assistance system, and having sickness insurance.
Immigration was a massive red herring in the referendum campaign.