A few years ago, one of the banks got itself into a legal muddle when it failed to get both parties to a mortgage to sign. It was then not legally permitted to repossess the house when the mortgage payments were not paid by the borrower, since they had not got the other joint mortgagee to sign the form.
The courts threw out the bank's application for repossession on this legal blunder. Banks' paperwork got sharpened up considerably in the light of that legal decision!
The tenancy you describe seems equally confused as to who guaranteed what to whom.
The proper advice would be to consult a solicitor, though he/she might find it difficult to give a legal opinion without proper written evidence.
I can only suggest (as a non-lawyer!!) that you consider the following approach to the current agency:
"Please produce written copies of all valid tenancy agreement documents that I have signed that contain within the terms and conditions the requirement for me to give you more than one month's notice of terminating the tenancy, as I wish to discuss the matter with my solicitor. If I do not receive these documents within 7 working days, you will be deemed to have been unable to produce any such valid document to support your claim for more than one month's notice, and I shall treat my tenancy as having, and as always having had, a notice period of one month only. I look forward to your early reply, as time is of the essence."
Send this by recorded delivery, and retain a copy which you could show to a solicitor, together with proof of posting of the letter to the agency.
If they do not reply, write to them again by recorded delivery after 7 working days, as above, and say:
"Further to my previous letter dated ../../.., and your failure to respond within the stated period, I hereby give you ONE month's notice of termination of my tenancy. Please note that any further attempt on your part to press for a longer period of notice is now out of time, for the reasons stated in my previous letter, and I must advise you that legal proceedings may result from any attempt to require notice exceeding one month."
If they DO reply with copies of paperwork, however, and if it does clearly state TWO MONTHS, then I'd be inclined to give 2 months' notice - though the legal muddle in the documentation, if as you described, may well have rendered the whole tenancy invalid. Try to avoid actual legal fights over just one month's notice, however, since even if you win, it's a tiring process - better to bluff your way towards your preferred outcome if you can!
Good luck!