I am not convinced there is a saving from it, more likely they want people to do this to reduce peak time demand, and one way to convince them is to tell them they will save money.
For the same reason a kettle is more efficient than a saucepan to heat water even though it has higher peak power draw.
What will save money is if people turn down room thermostats but as of yet the government has not issued this advice.
Central heating can be wasteful in itself as you have to heat all the pipes etc. thats all basically waste, anything that heats slowly/gradually in a home that has insulation issues will also be wasteful. But there has been for a long time assumptions that anything gas is cheaper than anything electric, usually based on that gas is cheaper per KwH, but not taking into account efficiency.
I am one of those who will wear more clothes before turning the heater on, and I do question the merits of heating my entire property vs just the room I spend the most time in.
My advice is seal windows, cling film whatever, turn down thermostat 1-2C, those should be easy wins without much compromise. Even just taping edges of curtains against wall is quite effective.