Zero-rate VAT is also the vat rate applicable to any admin fees where an agency fees-turnover is below circa £77k pa.
VAT becomes more complex when the agent or landlord is a shop owner who has elected within say a month of exchange of contracts to take advantage of the recovery of vat on the purchase. The downside is that VAT must be charged on rents related to such purchase.
This is in contrast to a neighbouring shop where there is no vat on the property in which case none is chargeable to the commercial tenants.
There are positive and negative consequences of VAT .
If agents and landlords are vat registered they can recover any applicable vat charged. The down side is that they will be at a commercial disadvantage since they will be somewhat less competitive on fees than their unregistered competitors, who would not be obliged to charge vat to tenant customers and landlord clients.