Whether you are charged VAT on rental payments depends on the particular property. If the landlord has ‘opted to tax’ for VAT purposes, then the rental payments will be subject to VAT; otherwise, rental payments are exempt from VAT.
If your business is VAT-registered, your costs will not normally be any higher whether the landlord has opted to tax or not. You can reclaim any VAT you pay, in the same way as you do for other business purchases.
However, if your business is not VAT-registered, or if you make VAT-exempt supplies, any VAT charged on rental payments will increase your costs.