Have a mass clean-up operation. No valid papers...out you go.
BIG fines for employers and those harbouring illegals.
Not going to happen. There is nobody in government with enough spine to reclaim our country from the millions of parasites currently sucking it dry and multiplying faster than the indigenous population.
Employ locals at proper wage levels. If veg prices go up, then so be it.
If you can afford to run a car, drink, smoke, and rent cable TV, mobile phone etc, then you can afford to pay more for your basics like FOOD.
Also: DO NOT grant British ctizenship to children born here of illegals or from other EU countries.
Want to breed ? Go home and do it.