If an instructor works EXCLUSIVELY for one school / club on a 'self employed basis', then a 'master and servant' relationship will exist. In this situation, HMRC will try to argue that that the relationship is in fact 'disguised employment'.
On the other hand, if an instructor works on a self employed basis for a number of people, he / she is genuinely self employed and HMRC can then have absolutely no issue with the arrangement.
Wrong on several counts.
Having only one client does
not produce a "master and servant relationship" or make you a "disguised employee" - employment status law is much more complicated than that, and people have won against HMRC in court despite having only a single client for several years. (You are however right that HMRC will try it on.)
Similarly, whilst having more than one client is a jolly good indicator that you are
not a "disguised employee", and the odds could well be in your favour, this is
not a magic bullet, and you could still be found to be a "disguised employee".
There is one very simple rule to remember about employment status: "there is no magic bullet", and hence no simple cases.