you cannot enforce the UK minimum wage on cheap labour hired in Bulgaria, Romania, or elsewhere in eastern Europe. So so much for your:

"Cheap labour can be dealt with by enforcing a minimum living wage"

No one said it is easy to do, but you certainly can do it. As with any other firm it is bringing action against the firm operating in the UK - in this case the gangmasters or whoever - based on what the workers receive. That the workers are only entitled to a certain amount under their contract does not override the amount they are entitled to by Law.

However, the real difficulty is the 'self employed' category. If these Bulgarians are technically self employed then they do not have the right to a minimum wage. So the solution lies in dealing with the abuses of the self employed classification and that is not only (or even mainly) workers from the EU. As we remember, we had many deaths of Chinese workers harvesting cockles. We also have delivery services and similar exploiting it to effectively deny workers rights like minimum wages, sick pay, holiday and so forth. The problem can be tackled, but it is not very closely connected to free movement to and from the EU.