Do you have the v5 or does the lease company have it? I would want to deal with the party named on the v5 personally.
I bought mine in the identical fashion. The finance was cleared by the owner who had the v5 prior to me taking the van. I had confirmation of this obviously in paperwork from the finance company declaring they had no interest in the vehicle now that the finance was settled.
This can all happen pretty much instantly with a bit of pre organisation.
The vat is payable on the first point of sale from new. Luckily the guy I bought from wasn't vat registered and he couldn't pass the vat on to me. Most vans are sold by people or companies or indeed Ford who are vat registered so to find a van free of vat ( under 6 months old in my case) is pretty rare. So as long as you don't get greedy with the price it will sell very fast usually.