The SLAE "report" is pretty thin - more of a polemic from a red-top newspaper than a serious analysis.
One of my hopes for post-Brexit Britain is that immigration is limited. It's these zero-hours contract jobs on the minimum wage that are fed by new arrivals. Often single people, they can live cheaply, and are prepared to work hard and conscientiously for little pay and no guarantees - but often for far more money than they can earn in their home country.
If the supply of cheap labour was limited, employers would have to improve pay and conditions to retain staff. Those that didn't would lose business.
This sounds like a long-term hope, but I firmly believe that it could be a positive spin-off from the cessation of "freedom of movement", which has fuelled the current surge in low-security, low-paid jobs.
And I speak as someone with first-hand experience of this end of the jobs market.