Is this work being done on a house that is and has been empty for 2 or 10 years? Eg so that it qualifies for reduced VAT?
If not then I agree you will have to pay the VAT
You can't buy the materials without VAT yourself.
They can't buy the materials and sell them to you without VAT (if VAT registered).
Being VAT registered allows all companies to reclaim VAT. Next time you buy a dishwasher ask the shop if they will knock the VAT off and see how it goes 🙂