Tim Martin does not require special treatment, he will able to attempt to justify any call for migrant labour just like any other company. Short term contracts would be ideal. His non UK business is less than 1% with no openings in the EU in this financial year so a red herring. I find it strange that you think UK businesses should not trade in Europe.
I think I see what you are driving towards. A mass of civil servants whose job it will be to deal with requests from all the pubs, restaurants, hotels, care homes, hospitals etc. to be allowed to have the staff that they need. Will they be given quotas as to how many they can employ during the course of a year, or will they apply on a week to week basis? If the former what happens when they have used their allowance up? We have seen hospitals filling posts for doctors, only to be told that they cannot have a visa, so the patients are the ones who do not get the care they could have had.
Your scheme has the makings of a state controlled economy governed by numbers that can be employed. I didn't think you liked state control.