The City of London will pick up your asbestos (service run on behalf of all London boroughs) - details at https://www.cityoflondon.gov.uk/services/environment-and-planning/waste-and-recycling/household-waste-and-recycling/Pages/Hazardous-Waste.aspx
Many civic amenity sites don't accept asbestos.
Ah, it's different out here in the sticks.
@Bobbo started
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The City of London will pick up your asbestos (service run on behalf of all London boroughs) - details at https://www.cityoflondon.gov.uk/services/environment-and-planning/waste-and-recycling/household-waste-and-recycling/Pages/Hazardous-Waste.aspx
Many civic amenity sites don't accept asbestos.