Immediately, if the local authority is the landlord. The TMO might have assumed responsibility for managing the building, but ultimately liability for a failure to comply the the landlord's repairing obligations will still rest with the landlord.
Check who your Ward Councillors are.
Email them all. They won't see your email, but their aides will.
Also check to see if any of your Ward Councillors are Cabinet Members.
CM's internal emails are less ignored/dealt with quicker than those from other Councillors.
Immediately, if the local authority is the landlord. The TMO might have assumed responsibility for managing the building, but ultimately liability for a failure to comply the the landlord's repairing obligations will still rest with the landlord.