What is the effect of previous predecessors in title being admitted in title?

The very old rule about admissions by predecessors in title was pressed upon us, relying upon Woolway v. Rowe (1834) 1 Ad. & El. 114, 110 E.R. 1151, 3 L.J.K.B. 121. That is not a case on examinations for discovery, of course. It involves declarations as to ownership or non-ownership of one parcel by the former owner of the fee which is now held by the party against whom it is sought to use the declaration. In argument, Parke J. said that such admissibility depends upon privity of estate, and would not apply to two successive holders of a bill of exchange. The relevant part of the decision of Denman C.J. is only one or two sentences long. Aside from also mentioning privity of estate, it gives no reasons and cites no authority.