Sounds like the house was originally fitted out in a very odd legacy electric heating configuration that was only supported by a very limited number of specialist tariffs from a couple of suppliers. Think of the 'Heat Electric' adverts from the 70s...and if you are too young, they are on Youtube!
The tariffs are long gone, as are the types of system you have.
Your meter is essentially two meters within the same enclosure, hence why you have two MPRNs. Your main half of the meter is a conventional enough dual rate (Economy 7) meter which powers everything that connects to your consumer unit. The second half of the meter connects via a time switch (possibly mechanical but more likely radio controlled by Radio Tele Switch) to your old storage heaters. The original tariff would have billed you for day/night rate on the conventional house electrics and had a special deal for 8 hours off-peak heating, plus a 3 hour 'boost' during the day.
Your four readings correspond to 'Day Use', 'Night (off peak) Use', 'Night heating Use' and 'Day Heating Boost Use'.
This system is so legacy that Noah possibly had one on the ark. Even the couple of companies that have taken on, or grandfathered, these old early 70's setups and tariffs are desperate to completely phase them out.
If you completely removed the switched heating system, including all wiring as far back as the meter itself, you could argue the case to have the meter replaced with a standard meter. This can then be upgraded to a smart meter later on. That said, your meter will be so out of date and outside the certification period, it should have already been replaced by now several times over...
Once you are down to a single meter, you can apply to have the second MPRN removed. As it stands, with two MPRN's you are paying 2x the daily standing charge.
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theunknowntech will be able to give you a little more info, I'm sure, because metering is his thing. I'm just a humble electrical engineer.