A tiny nitpick - companies may not have to pay VAT on goods they purchase to then sell on, but they do however have to pay HMRC VAT on services that they provide.
For service based VAT registered companies (like my own limited company), HMRC operates a VAT flat rate scheme whereby you invoice the full prevailing rate of VAT, but you pay to HMRC a lower rate of VAT to offset the fact that you are still expected to pay VAT on any supplies you purchase.