have a 15ft by 10ft asbestos monstrouserty in my garden, this summer was planning on getting rid of it and putting a 26sqft bricked summer house in its place (office / boys room), quote for that came in at £8k and to remove the asbestos shed, i got a guy down to £1100
a few people had said just damp it down and dispose of it in council bags, but the bag are quite small you wouldn't want to be breaking up 4ft x 3ft asbestos filled sheets to cram into those bags, not worth the risk, even if you do get someone else to do it