Welp, it's taken an age, but I finally got the car in my hands again and successfully found the problem, it was indeed a broken wire. See attached picture, where I stripped the brown wire back to find the break. Knowing that from the previous time, I wasn't getting a signal at the connecter pins, this time I stuck a pin into the brown wire further back to see if I got a reading on the multimeter and I did.
So, I stripped the wire back and just touched both ends together to see if it worked, the first good sign was that the fan was no longer turning on as soon as I turned the engine on. Secondly, I connected my OBD scanner and used the OBD Doctor app to check the Engine Coolant Temp, it no longer reports -40c, but if I break the connection, it shows -40c and the fan switches on.
If the garage can squeeze me in, I'll get them to solder the wires as I'm useless at that. Then a nice long test drive to check temps, the fan kicks in when it's supposed to and we finally get some decent heat in the cabin.
Next step is to try and flush the coolant as it's brown and there's horrible sludge in the reservoir :/ Problem is, I can't see if there's a drain valve on the radiator and I can't feel one either. Will I have to just disconnect the lower hose going to the radiator?
Anyway, thanks again for all your help, especially you AUTOSPARK