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In some of the stronger voting areas for exit such as east anglia the minimum wage as such does not apply for a lot of jobs.
The reason and I speak from personal experience is especially fruit picking etc. you get paid say per 20kg. If this is say £1 and with the best will in the world and being young and fit you at best can only manage five 20kg per hour the fact there is a minimum wage is irrelevant.
You'd need to make it something that could be reported to HMRC by the worker, which would trigger an immediate forensic audit of the employer.
If the employer was paying the correct wage then the employee loses their job (and likely will find it hard to get a new one), if the employer was found to not be paying the correct wage then some sort of crippling fine/other scorched earth penalty.