Hardcore and rubble
Hardcore can be taken to one of north London's reuse and recycling centres (RRC) where it can be recycled. Each north London household can take up to six standard rubble sacks of soil/rubble to an RRC each month. This includes concrete, brick, stones, pebbles, soil, sand and gravel. A standard rubble sack is 51cm by 76cm (20 inches by 30 inches) or equivalent.
If you have a large quantity of hardcore material, consider hiring a skip.