Minimum wage is law. If they're not paying it then they stand to be taken to court. You assume that British people will always do the jobs that EU migrants will do. In the majority of cases they will and UK and EU workers will work side by side. When I worked on building sites I worked alongside many Eastern Europeans and we were on the same rates. The problem my trade had was a lack of qualified and skilled workers, this was made up with EU migrants. I know plenty of people who do warehouse work and work alongside EU immigrants all on the same rate and better than minimum wage. I know a supervisor at one of the big warehouses in Rugby and they simply don't get enough UK applicants to fill their workforce. Then you have service sectors, again can't get UK applicants. Then you get seasonal farm work, again, where are these UK applicants willing to do the job?
I never claimed that EU migrants are all earning the living wage, some are and better but even then the point still stands. Who's surpressing wages in the UK when we have a minimum and living wage that the government can raise at will?