Here is a very useful summary from a DECC report of the effects of price motivators on the extent to which domestic electricity users alter their consumption patterns.
There is one clear message:
They hardly do at all!
As predicted by Alex Laskey of Opower, consumers do not react to this sort of price message! (Interestingly, though, the average reduction is about 14%, which is what is needed to eliminate the early evening peak).
People react to peer pressure - so the useful communication is:
I shift my electricity time-of-use out of peak times, do you?
Tell your friends!