The bureaucracy associated with checking entitlement to work is pretty horrendous, and of dubious benefit. In the absence of the minimum wage, there might be some justification for preventing forwign workers from under-cutting British citizens, but we have had a minimum wage for years now. So what is the point of such restrictions. If non-UK nationals wish to help grow our economy and contribute taxes, why should we stop them?
Scrap work permits. If people reside in the UK (permanently or termporarily) then let them work.