You need your public liability like you already have,
salon and stock insurance to cover you for any break ins etc,
if you buy the salon buildings insurance, if you rent this is usually the landlords responsibility,
an accident book for just in case,
employers liability if you are going to be taking on staff or work experience students from college,
health and safety is a poster that you display and can be bought from most stationers,
need to let inland revenue know within 3 months,
check what your business rates will be before signing for any salon (varies from shop to shop) and make sure you get in touch with your local council straight away so you can apply for small business relief (this will save you £100s)
that's all i can think of just now from the top of my head but hth :hug: