Steve Shaw:
The national minimum wage
The national living wage and national minimum wage set minimum hourly rates that employers must legally pay workers in the UK.
Check your pay rate
The national living wage and minimum wage does not apply if you are genuinely self-employed.

Unfortunately, quoting from a Union's website may not always get you a full or factual answer.
From HMRC Here the list of those who may not be covered by National Minimum Wage is somewhat longer:

The following types of workers aren't entitled to the National Minimum Wage or National Living Wage:
• self-employed people running their own business
•company directors
• volunteers or voluntary workers
•workers on a government employment programme, such as the Work Programme
•members of the armed forces
•family members of the employer living in the employer's home
•non-family members living in the employer's home who share in the work and leisure activities, are treated as one of the family and aren't charged for meals or accommodation, for example au pairs
•workers younger than school leaving age (usually 16)
•higher and further education students on a work placement up to 1 year
•workers on government pre-apprenticeships schemes
•people on the following European Union programmes: Leonardo da Vinci, Youth in Action, Erasmus, Comenius
•people working on a Jobcentre Plus Work trial for 6 weeks
•share fishermen
•prisoners
•people living and working in a religious community

Work experience and internships

You won't get the National Minimum Wage or National Living Wage if you're:
•a student doing work experience as part of a higher or further education course
•of compulsory school age
•a volunteer or doing voluntary work
•on a government or European programme
•work shadowing