Without any sensible manual it's hard to tell what your charger is doing, but it is advertised as a reconditioning charger. So if it started to charge a very depleted battery it may well have tried to "recondition" it by holding the voltage higher than normal - though that voltage if accurate is still very high.
If the voltage has settled such that the battery seems charged I'd try the full disconnect reset a couple more times. And make sure it's a full disconnect not just the fridge switch looking at other folks threads.
On a balance between a simple voltmeter and the voltage sensing of the fridge I'd give more weight to the fridge, ideally get a decent enough multimeter so you can cross check the fitted meter.
I would also recommend that you get your mains charger changed as soon as possible. An £18 unbranded maintenance charger is not the thing to rely on while camping. The Victron chargers are well regarded but NoCo and CTEK are other choices. With an 80Ah battery something around 7-10A would be ideal.