As a tenant you have the right to request your landlords address details. In your case this would be via your letting agent and they have 21 days (note as it does not state calendar or business days I would expect this to be interpreted as calendar days) to provide you with these details.
Depending on what part of the country you are renting the property will depend whether you request the details under Section 1 of the Landlord and Tenant Act 1985 (England and Wales) or Part 16 section 327, subsection 1, of the Housing (Scotland) Act 1987. Below are the links for both parts of legislation:
There is a template for the 1985 act below (just ensure you quote the correct type of tenancy agreement)
I recently had to exercise this right in Scotland, and basically amended the above template in conjunction with the legislation in Scotland. The agent (one of the largest in the UK) was very hesitant to accept the document as it is quite legally worded, however I ultimately received the Landlords name and contact address within 30 minutes of the request…
Whilst in my case I did not have to utilise the new lettings code, I have had a quick look at the code and on Page 15 under the subject "Moving in (Inventory check in) point no.72 clearly states “If the tenant asks in writing for the landlord’s name and address, you must tell them free of charge within 21 days”. Again the link is below
Failure to comply would be a breach of such code. Hopefully that provides all the information you require and confirmation of how to uphold your rights!
Good luck with it and please pesevere !