Yeah they will always give you lower price. I'm shocked they offered you £850 though, they was only going to give £650 for a 2.1 v6 Jag on an 02 plate part X.
I would say private sale be looking at anywhere from £1000 to maybe £1200 depends on a few things like the service history and so on but that's what I would say you would be looking at as a very rough guess