Overkill perhaps but: I used steel studs resin anchored far into the brickwork. I didn't want any load putting on the plaster which is old and fragile.
For the floor units the studs connect to steel brackets screwed to the units. The wall units hang in the usual way from metal plates bolted to the studs.
Since the floor units are secured by the resin studs to the wall I could probably do away with the legs and plinth altogether and let the floor units 'hover'. Might look stylish with a light underneath..
Robert