You could use the private sale element to benefit both of you and negotiate a figure that will save you and them money.
For example, if the property was sold for £500,000 and the estate agent would otherwise charge 1.5% + VAT in fees, the net sale for the vendor would be £491,000.
The buyer would have to pay £12,500 in stamp duty, so the cost to them is £512,500.
If the vendor were to sell privately for, say £495,000 there's no estate agent's fees, so they're £4,000 better off.
You, as buyer would pay £12,250 in stamp duty, bringing the total cost to £507,250, so saving £5,250.
It could be structured therefore to meet half way and save you both money.
(The above stamp duty calculations are on the assumption that you're not a first time buyer - if you are the figures for this are lower - take a look here - Calculator)