Abstract: A bracket assembly, for use in spacing apart the inner and outer membranes of a cavity wall or roof construction, consists of a support member attached to an inner lining membrane and having a C-shaped cross-section and a bracket element formed from a trapezoidal shaped metal plate. The bracket element has the longer parallel side bent through 90.degree. for attachment through the outer membrane to a building structural member. Two inwardly directed slots are formed parallel to the opposite side to form a T-shaped head to the bracket for engagement with the C-section member through a twisting and locking action.