@Madrab has given a good answer, however how the property is used, and what tariff is used, can impact on how well it works, there are special tariffs for heat pumps, but where is all gets muddy is when there is something else also needing a special tariff.
So heat pumps, EVs, Solar panels, batteries, and storage radiators all can benefit from off-peak supplies, but not always the same off-peak tariff. Some give 5 hours, some give 7 hours, some have three stages, some only two, and some have just one cheap slot, and other three cheap slots etc.
And we have seen with storage radiators how the tariffs have changed over the years, so back in the 70s the off-peak was very good, but over the years the rates have changed, so we are taking a gamble on what will happen in the future.
I went from a cylinder for domestic hot water (DHW) to a gas boiler in the last house, as it allowed me to use the room it freed up, it did however have some downsides, it took a lot longer to get hot water to the taps, and any problems with water supply resulted in no stored water, so no water.
As to cost, this house with a cylinder, we are paying far less with an immersion heater to what it would cost using oil. But it depends on the house, mother house boiler right next to kitchen sink, so to that point, got hot water faster. There was a problem with the shower, with it going from cold to hot back to cold and then hot and stay hot, as the reservoir was used up, but with a wet room could easily stand to one side as it warmed up.
Again we use solar here to heat DHW, the regular spikes
is the immersion turning on to keep the DHW hot, using the solar power, I actually think it would cost less to just use off-peak, but to change the system will cost, so sticking with what I have. I have seen a huge drop in oil use since using the solar, I had no idea how much DHW was costing me.
As to how much it costs for the match with a combi boiler I don't know what I am talking about is cost to fire up the boiler even when no hot water gets to the taps, it is a phrase used with heritage railways, how much it costs to get up steam, even when the engine is not used. But I do not use enough hot water for the water in the pipes to stay hot between each use, so mothers house I would hear the boiler fire up when I turned on the tap, in Eco mode, and I would get half a bowl of water before the hot arrived, I also had to turn on the taps full on, or the boiler would not fire up. And turn Eco mode off, and the boiler would fire up every so often just to keep the reservoir hot. And all the metal in the boiler has to heat up and cool down again, so either way we need some energy just to have DHW avaiable.
