The landlord actually doesn’t have to tell you anything unless you make the specific enquiry.
It is a criminal offence not to have a Gas Safety Certificate.
Here is one website http://www.airintelligence.co.uk/commercial-gas-safety-certificates-one/
From which you will see it says:
Your lease or a separate contractual agreement can help to set out practical arrangements for ensuring gas safety requirements are met. However, the ultimate legal responsibility remains with the occupier of the workplace concerned.
The owner, or other person in control of the building, may also have duties under the Health and Safety at Work Act 1974 – such as ensuring heating equipment in common parts is maintained safely. The lease or separate contractual agreement can be used to determine how these responsibilities are allocated.
Which confirms what I said.
If there is no provision in the lease then as it says, it is the occupiers liability which is yours. To be honest, for the cost of getting the certificate, it pales into insignificance compared to the cost of actually going to court to get the landlord to provide one.
I don’t know why the local authority have got involved with the landlord.
In the final paragraph you explain the liability but don’t actually say who’s liability that is. I get the impression that it’s the landlord who has those obligations in which case that would explain why the local authority are pressing the landlord.
I don’t the whether you want to use this as a lever to leave or not but because of the cost of getting the certificate compared to the cost of leaving the property, it’s unlikely that it would enable you to do so although you could always try it and see whether the landlord decides to take issue with it.