The local authority has certain responsibilities, under the Mines and Quarries Tips Act 1969, for ensuring the safety of the public. However there are an estimated 300,000 disused mine shafts across the country so, with limited resources, local authorities will always struggle to carry out their duties.
However if you believe that a local authority is not carrying out a statutory duty, you should complain to the Local Government Ombudsman:
http://www.lgo.org.uk/making-a-complaint/
Chris