I think it's done with registers in the meter rather than a separate MPAN, whatever...
I guess it is reasonable that night time power costs less as there is considerably less demand for it. Which is why these demand-shifting tariffs have come about. I'm not so sure that the daytime rates should be called penal - they are just more expensive than night-time. It's only like holidaying in the school holidays v. term time - supply and demand!!
So people with the wherewithal to buy batteries can avoid the absolute peaks of power, but it does come at some cost. A sensibly sized battery array is now upwards of £7.5k isn't it? Which would have a few years payback time even with the expense of power these days. And if electricity prices fall considerably, or tariff structures change (to remove gas from being the determinant for electricity costs) who knows whether they will still be economically sound. If someone has taken that gamble, good luck to them. A bit like buying and EV - expensive to buy, cheap to run at the moment, but we don't know what the future might hold.
I did get somewhat flamed on another forum for suggesting that people with batteries and large solar arrays were gaming the system but that wasn't solely by shifting use, or storing cheap power for own use. At one stage it was economically sound to fill your batteries overnight then sell it back to the company the next day ( - it may still be true). I suppose if the company is still able to turn a profit then everyone is happy. But I did smile when people denied it was about gaming the system, r, instead using the justification that they are only interested in their carbon footprint etc etc. yeah sure they were... there was a even league table for who had benefited most!
I do feel very sorry for poorer people who get stiffed by companies and I wish there was something could be done to prevent it - but I don't know what.