As a condition for the renovation work on 36 to 40 Langham Street, Westminster Council required the production of a Historic Building Recording Report. This report features a section on Middleton Place.
The author suggests that the original houses in Middleton Place, built in 1759 in the tail end of the reign of King George II, may have been rebuilt prior to new leases being issued in 1856:
The full report (split into three parts) can be found here.