Kenwood: dressing area.

Cynthia, in her most recent autobiography, specifically remembers the "his and hers" basins in their bedroom suite - and sure enough, there they are on the '64 plan. Richard Hall, in his account of meeting John at Kenwood, recalled seeing John shaving through an upstairs window - so that must have been one of these:


In 2006, this part of the house was being used as a study:


It's also worth recalling that Joe Baiardi's video shows the dressing area, completely gutted, as it looked during renovation at the end of last year (around 07.27).