Slipslider, I was actually asked to add VAT to my invoice by one of my clients and I questioned it as previously I had not added VAT to expense claims. I was having a VAT inspection at the time (Not fun!) and brought it up with the VAT inspector. He said that yes it is quite correct that you should add VAT to an expense invoice - I dont follow the reasoning as HMG ends up with two lots of VAT.
Only getting charged 12.5% does sound very dodgy though and you may get some joy by questioning them on why the descrepancy in case they are keeping it.
Julian.