Legally you can not drive a car without MOT, which makes difficult to sell a car without MOT as you can not drive the car to the buyer's place.
You need to find a buyer who is willing to come to your place and pick up your car. The following online car dealers are buying any types of cars:
www.webuyanycar.com/
www.sellthecar.com/We-buy-any-car.aspx
www.dealerbid.co.uk/

You have to inform DVLA when you sell or scrap your car, otherwise, you will be responsible for the taxing even if you do not have the car.