However, those involved in unearthing the material are believed to have been ''at very low risk'' and health checks were deemed unnecessary, council infrastructure and networks general manager Ruth Stokes said.
The material containing asbestos fibres was unearthed as volunteers worked to extend the BMX track last week.
The area was cordoned off and samples taken, which returned only one result above national guidelines, Mrs Stokes said.
The council had taken a ''conservative approach'' in fencing and covering the find to ensure there was no risk to the public, she said.
The material came from part of an old landfill site and the council considered burying it again to be ''the best option'', she said.
''Our consulting experts are preparing the remediation plan over the next few days, with work likely to be carried out in the next few weeks.
''The site is well secured now and there is no public risk with the interim measures in place.''
