In my previous house, we kept the E7 long after the storage heaters were removed, and had a few "off peak" sockets in the kitchen for the washing machine, dishwasher and tumble dryer.
While ANY socket will get the cheap rate with E7, you would have to have a washing machine with a built in start timer, or wait up until gone midnight to turn it on. The dedicated off peak sockets would power up at night and the machines would start.
It was usually the much older "white meter" tarrifs that only supplied cheap rate to just the heaters. These had two physically seperate meters, rather than one dual rate meter.