Whirlybird is quite correct about the National Minimum Wage (NMW). It does apply to ALL empoyees in the uk. So instructors are not exempt. The body that is supposed to enforce the NMW is the Inland Revenue (IR). In practice the IR usually check this when they are doing any routine PAYE/NIC compliance visit to an employer. The Ir will also make a special vsist if it receives a complaint from a worker who considers that he has been paid less than the NMW. The IR will not disclose the name of the worker to the employer.
As such, the NMW does not apply to self-emplyed workers. BUT, under the NMW regulations, it does apply in those instances where the employer is deemed to have wrongly classified a worker as self-employed.
So, if an employer has been treating a worker as self-employed, in order to avoid those little inconveniences such as paying employers' NIC, paid holidays, AND paying the NMW, then the employer may get a double smack hand & penalties from the IR. Firstly for being in breach of the PAYE regulations & not deducting tax & NIC from the pay, & secondly for not paying the NMW. This applies even is the worker has agreed, with the employer, to be treated as self-employed.