its in the certificate terms that the LA can close (withdraw) at any time- there is also a section on the SAG.
https://sgsa.org.uk/wp-content/uploads/2018/09/Safety-Certification-Guidance.pdf
"If the chief officer of police believes that police officers need to attend a particular event, but the management of the sports ground disagrees, the local authority must consider whether the absence of police would adversely affect safety at the ground. It should consider any mitigating measures offered by the ground management. It is for the certificate holder to satisfy the local authority that the event can proceed safely without the police being present. If the local authority is not satisfied, it could close part or all of the sports ground or reduce its permitted capacity to a level that it considers reasonably safe for the event concerned. The options available to the local authority are described in section 7 below."
and I would be very surprised if it didn't have recommendations from the Saftey Advisory Group within the certificate.
However, the licence does not restrict the local authority from including whatever conditions in the safety certificate it considers necessary or expedient to secure the reasonable safety at the ground. The local authority could close or limit the capacity of a sports ground for safety reasons, notwithstanding that the area in question had been licensed by the SGSA
