The place I use, which is also (too!) conveniently local to me, is possibly the UK's biggest second-hand equipment seller - Ffordes of Beauly. They normally offer three ways of dealing - 1) straight purchase; 2) part-exchange; or 3) commission sale. Despite the 20% of selling price charge, the latter will give you the greatest return price, but you'll have to wait until it's sold - normally you'll receive a cheque about four weeks after it sells. In my experience, somethings go really quickly, whereas others may sit there a while. They'll advise on price etc., from which you can decide to go higher or lower, depending on the return your seeking, and/or the desired speed of sale.
Probably could earn more by selling it through the likes of Ebay, but that brings other risks, and my choice has been to avoid such potential hassles! You, and your profile would be providing the guarantee to subsequent purchasers, rather than the shop.
Website:
http://www.ffordes.com/
Current Fuji X-series cameras for sale (might give an idea on prices etc.):
http://www.ffordes.com/category/Digital_Cameras/Mirrorless/Fuji_X_Series/X_Cameras
Details of their commission sale process etc.:
http://www.ffordes.com/Commission_Sales
And details of used equipment grading:
http://www.ffordes.com/Used_Grading
(Note - They're NOT open at the weekends... and I'm not on commission! Also, other camera shops more local to you, may similarly deal with second-hand items.)
Best wishes, good luck with your sale, and better luck with any other camera you choose to try!