Hi, my son has the same issue with old evidence of water ingress through light fittings, now showing mould spots, still not resolved.
I agree with AnthonyB. You are getting the runaround. The letting agents have to give you the name and address of the landlord if you request it formally. That just means asking for it in an email btw. They have 21 days to comply. It's my understanding that it is 21 days not 21 working days.
Don't accept being told that the LA is the landlord or acts for the landlord so it's a 'care of' address or their offices. You have a right to know where the landlord is. It doesn't have to be their home address understandably, but an actual address (their place of work for example).
Your tenancy agreement should have a service address for the landlord in England or Wales. This can be the agent. But ask anyway.
Useful read but long: https://www.legislation.gov.uk/uksi/2020/312/contents/made
Also:
Written requests for landlord's name and address
The tenant can make a written request for the landlord's name and address from the:
landlord's agent
person who demands, or last received, the rent
This information must be provided in writing within 21 days.[5] Address means the landlord's place of residence or place of business or, in the case of a company, its registered office.
If the landlord is a company, the tenant can make a written request for the names and addresses of the company's directors and the company secretary. The request can be made to the:
landlord (the company)
landlord's agent
person who demands, or last received, the rent
This information must be provided in writing within 21 days of the written request.[6]
There is a penalty for a failure, without reasonable excuse, to provide the information as set out above. The landlord, agent or rent collector, as appropriate, can be prosecuted by the local authority and a fine of up to £2,500 can be imposed in the magistrates court.[7]