The minimum wage does not apply to company directors unless they also have contracts that make them workers. Company directors are office holders in common law and can do work and be paid for it in that capacity. This is true no matter what sort of work is done or how it is rewarded.
However, company directors who also have an employment or worker's contract with their company will need to be paid the minimum wage for work done under that contract. If a company director is unsure whether they have entered into a contract with their company which makes them a worker for minimum wage purposes, they may wish to take independent legal advice. See employment status of company directors and choose a solicitor for your business.