The wholesale price might change but the retail price is constant. Most people wouldn't bother to change their useage as they pay the same all the time. The supply companies would have to change every meter in the country to get a system of variable charging to work.Power prices on the wholesale market change every 1/2 hour and yesterday (25th) prices ranged from 1.809p/Kwh at 04:30 to 7.552p/KWh at 17:30 i.e. the 17:30 price was 317% more than the 04:30 price. Until they give out this info the grid is going to peak at 17.30 every day and large inefficiencies will result.
If the nation went onto flexi time many things would improve, such as traffic congestion. Same if mum's walked their kids the mile to school (another topic). If the TV companies varied their times for commercial breaks, there wouldn't be a spike as the kettles went on. Do we legislate for it? Even if we did legislate for flexi time, how many people would actually change their habits?