Who was the other?
Jeffrey is known by us to have been at Kennington Lane.

His body was found on the following morning in the room at New Inn.

No third person is known to have come from Kennington Lane; no third person is known to have arrived at New Inn.

The inference, by exclusion, is that the second person--the woman--was Jeffrey.
"Again; Jeffrey had to be brought from Kennington to the inn by John.
But John was personating Jeffrey and was made up to resemble him very closely.

If Jeffrey were undisguised the two men would be almost exactly alike; which would be very noticeable in any case and suspicious after the death of one of them.