Could be a cost thing if their own tax affairs are simple. Your fees to the company are tax deductible (and some/all of the VAT might be as well), those to them individually are not. Therefore the personal cost is quite a bit higher. One of the many odd anomalies in our tax system.
You would think it was all about NMW - it would seem pretty pointless if that wasn't the aim. But it can't be. As the gov.uk website says "The hours that must be shown on a payslip are a separate matter from the number of hours worked for National Minimum Wage (NMW) purposes". They may not even be the same.
You can buy cotton or linen suits, guys. Don't have to go black wool.