I've just been having another shufti through my Railways of Beckenham book (well I would, coz it's local, innit?) and there is this wonderful picture on page 139 of a 4-wheel 3-compartment brake third. It looks just like the Hatton's 4-wheel brake coach as far as the passenger accommodation is concerned, but there is no ducket for the guard, and -- wait for it -- a birdcage on the roof. It is close-coupled to a coach, the first compartment of which has a big 2 on the door.
[The book is Andrew Hajducki, The Railways of Beckenham, The Ardgour Press in association with Noodle Books, 2011, ISBN 9781906419592.]