Been looking into this myself, having recently paid through the nose for private waste collection.

http://www.bromley.gov.uk/info/531/recyc...ing_centre

Pertinent section : "Bromley residents will be charged if they want to dispose of soil, brick, rubble, DIY and construction waste according to the weight. Currently, the minimum charge is £20 and vehicles will need to use the weighbridge for an exact price. Users not living within the borough will be charged £3 per visit."

I've not tried this yet so i'm not sure about the weighing - but I still think it'll cost less that what waste collection companies charge..