No, you can't claim the VAT back if you are not VAT registered.
Also, if you're on the flat rate scheme for VAT, you can only claim the VAT back for capital purchases of over £2000 in one go.
If you are definitely going to be under the VAT threshold, then I'd advise *not* to register for VAT... as if you *do* register for VAT, then you have to charge 17.5% VAT (20% come January) on everything you do - and that's even before you start thinking about income tax and national insurance - which would be paid from your income net of VAT - before you even get a penny!
For most people in the beauty industry, a significant expenditure is going to be time (therapist wages etc) - which will generally be greater than product costs. In which case you'd almost certainly pay more to the VAT man on VAT on top of staffing costs than you'd get back from the VAT man by claiming VAT back on products etc... in which case it's just not worth it - especially given the additional accounting complexity and the hassle of having to submit quarterly VAT returns!