If you are self employed you can set your own prices, the salon has no bearing on this at all.
I don't think HMRC are stopping self-employed in salons. What they are targeting and clamping down on, or so I believe, are salons that are VAT registered. They should be adding VAT to invoices for self-employed people and declaring it. From my understanding some salons use the self-employed route as a way of getting out of paying VAT.
Therefore, if the salon is VAT registered any self-employed people will have VAT added to their bill.
This is how I understand it but I am sure a more knowledgeable Geek will come along and advise accordingly.