We are first time landlords and have used a letting agent manage our tenant
We got six months commission free and have just got our first statement including the commission
The commission is 10% and this works out at £49.50
However we have had a deduction of £49.50 plus VAT
Am I being naïve in thinking that there should be no VAT on this deduction?
In essence I am paying the agent his fee and paying VAT for the privilege?
VAT is charged on both goods and services. You're being billed £49.50 for a service, so there's VAT to pay on it. It's just the same as selling goods at auction. The auctioneer will charge, say, 15% of the selling price for his services but you have to pay VAT on top of that, making 18% in total. (In your case it's 10% + VAT, so that's 12% in total).
I found letting agents so bad - not only VAT - but their total lack of doing anything besides taking the commission - that I do it all myself. Mine used to ring me up and say " the window is broken you have to get it fixed, OK ? bye. " and I concluded that I could do without them