There are three problems with the date on the plaque on the front of the building.
Firstly, the coat of arms is that of the Tattershall family. But the estate had passed through marriage from the Tattershall family to the Roper family in the mid-15th century.
Secondly, the initials 'WR', for William Roper, are cut in brickwork in the upper Tudor Barn indicating he was the builder. He lived there from 1495 to 1577. And the architecture of the Barn is consistent with the style for the first part of the 16 century rather than the later part.
And thirdly the plaque, now badly weathered, looks as if it it has been inserted into the brickwork at some later date.
Perhaps it could be speculated that William Roper, then 73, found the old Tattershall coat of arms, depicting three tigers viewing themselves in mirrors, and had it placed on the wall as a reminder of his ancestors. The Barn, of course, was an outbuilding to the main mansion which was positioned in the middle of the moat until its demolition in the 1730s, a new house then being constructed between the moat and Well Hall Road, this in turn being knocked down after E Nesbit left in 1922 and the estate being bought by the council in 1930.
This interesting piece of detective work is contained in a pamphlet produced by the Metropolitan Borough of Woolwich in 1936 to accompany the opening of the Tudor Barn as a library, art gallery and museum on 23 May 1936. The pamphlet is available from the current Eltham library and describes the building in some detail.