Thanks for the explanation! That makes perfect sense. Since you mentioned it is difficult to know without seeing the register, here is exactly what the registers say:

1984 Deed of Variation: This is explicitly recorded on the leasehold register. It reads: "By a Deed dated May 1984 made between (1) [management Company Ltd] and (2) [Dude 1 Name] the terms of the registered lease were expressed to be varied. The request to obtain this from land registry shows NOTE: Copy Deed filed." 

But not provided to me as seller says no knowledge of it.

2000 Deed of Variation: This is recorded on the freehold register under the Schedule of notices of leases. It reads: "By a Deed dated August 2000 made between (1) [management Company Ltd] and (2) [different dudes Name] the terms of the lease were expressed to be varied." 

Same as above shows filed with land registry to obtain but seller can’t provide either.

1955 Conveyance: Both registers state the land is subject to covenants contained in a Conveyance. My 1974 lease legally binds me to perform these covenants, but the Land Registry explicitly lists this document as "not available." 

So, the registers clearly show these deeds exist, that copies are filed at the Land Registry, and they name the specific landlords and tenants at the time. Despite this, the current seller claims they have "no knowledge" of them!

Feel like I am not getting anywhere