I participated in Octopus's trial scheme for this. Because we have smart meters and I'm the sort of nerd who cares about energy (the financial reward was laughable). We were give 24 hours notice of 2-hour windows and a target percentage of our average consumption for that period over the previous n weeks.
My conclusions:
-It was easy enough to reduce load by not cooking or washing at peak times. Either by changing your schedule a bit, or cooking a less energy-intensive meal that day.
-Morning or late evening energy consumption could be reduced somewhat by staying in bed or having an early night, assuming there wasn't something you *had* to do at that time involving washing/tea drinking/using a computer.
-It was basically impossible to make a significant dent in middle-of-the-night baseload, without doing things like turning off the fridge and shutting down network/alarm infrastructure.
-Crucially, you had no idea whether you were meeting the target in real time. Those stupid in-home display things don't do the right analysis. I wrote a program that could, based on my own monitoring of the meter's blinky light. Most people would only have known if they hit the target n days later when Octopus crunched the numbers. So if you're in it for the money, you can't rely on it. And you might inadvertently wash your hands causing the boiler to run and miss the threshold.
Ultimately, like most things energy-related, it's mainly the rich that benefit. Solar panel subsidies benefit people who own roofs, but made sense in terms of stimulating the industry and making solar systems better/cheaper. This sort of load-shedding bonus benefits people who have smart meters (which is more about luck and not reading the daily mail than wealth) and who are sufficiently educated and technically competent that they can control their energy use in a reasonable way. Roll it out widely, and you're going to get people unplugging their phone chargers and expecting a payment, or turning the power off at the fuseboard and falling down the stairs with a candle. Maybe that doesn't matter, and there are enough energy nerds that this sort of scheme can make a decent dent in the peak load on the grid, which ultimately benefits everyone.
Personally, I think this is only going to work on a wide scale if it's automated. That means internet-of-shit devices that can factor in grid demand when choosing when to run.