This is how I remember it working for self-employed,
Schedule D numer and NI Number, and OWN tools.
Used to work in an industry where my laptop was all I needed, so own tool.
I also have used SE persons for finishing some jobs, as long as I have had a schedule D and NI number from said persons then don't see what the problem is and don't really see where HMRC will have a problem, it is when you start to use a SE person 52 weeks of the year and you are their only employer, then it get's a bit messy.