If the materials supplied are zero-rated in the UK and are supplied with a VAT invoice to that effect, then I can't see how you will wind up with a VAT bill here, as you have met the VAT obligations in the supplying country, as per EU laws.
With regard to supply and fit, have them invoiced seperately, zero VAT on the materials and 15% UK VAT on the fit, once the invoice is issued by and paid to a UK registered company.
Never been through the experience, but it sounds tempting.
Now let the fun begin...