The landlord owns the property and an agent is someone who normally acts on behalf of the landlord and may do more of the day to day running of the property. They are usually the main point of contact for you as a tenant.
Tenants are entitled to the landlord’s contact details including address and the landlord is still legally responsible for the property. The agent has to give you the landlord’s details within 21 days of your request.
Check your contract to see who you have legally signed with, they will be responsible for carrying out any repairs and returning your deposit. If it is the agent, then they are responsible for looking after day to day repairs, but if there are problems with this, it would be worth letting the landlord know. If your contract has the landlord’s contact details then they are who you need to contact if you need repairs.