Yesterday evening we parked up with the battery registering 13.8V.
13.8 V is the float voltage for lead acid. That's a voltage that the battery can happily "coast" at without over-charging, but it
has to be pushed up that high: either charged from an external car charger or the car's DC-DC, or it's settling towards a resting voltage after having been charged in the last (very roughly) hour or two. So you can't use any voltage over about 12.8 - 13.0 V (depending on exact chemistry, temperature, and perhaps a few other factors) as any sort of indication of the state of charge (SoC) of the auxiliary battery.
Later in the evening it was down to 13.0V, measured via the MG Smart app.
In other words, later that evening it was pretty much at 100% SoC. It's full.
Now (lunchtime), it's down to 12.2V.
12.0 V in a nominally 12 V battery is close to dead flat, perhaps 20% SoC at most. 12.2 V, depending on many factors again, indicates a low, but not drastically low, voltage, but ONLY if it's been resting (next to no load or charge for hours). If you're measuring this in the car having opened the doors, then all sorts of computers have woken up, you may have some lights on, and if you use the start button to turn the car on (so you can see the 12 V reading on a screen for example), then radio, screens, perhaps the blower, and many more computers.
To meaningfully compare SoC (e.g. to see if the battery has self-discharge, or perhaps there is a "phantom" auxiliary battery drain), then you really need one of those battery monitors, or perhaps leads accessible outside the car to connect to a multimeter without opening a door, and not even approaching with car keys in your pocket. The car keys will probably wake up the body computer.
1) The mobile signal in North Devon is pants at best and where we were is next to non-existent. I am wondering if the car was trying to establish a mobile internet connection and draining the battery in the process.
That's an interesting theory, for sure. I'm doubtful, but I certainly would not rule it out.