Thanks again allI completely agree with KillRamsey's comment "Get out of full Auto", and, indeed, all the other advice posted here, including to shoot Raw. The RX100 will reward you handsomely when you've taken charge of it. As stated by others, changing cameras isn't going to solve the problem - that's just a way to lose money, and become disillusioned when things don't improve. However, learning to use the camera that you already have, WILL solve the problem... eventually. Study each photo; note what worked and what didn't; analyse the settings used for each, and the lighting conditions at the time. Then draw conclusions from that process. It's as simple - and as complicated - as that.
There are plenty of knowledgeable people on here who (as already demonstrated, above) will help if you have questions along the way.
Good luck, and show us the results of your progress...!
Without sounding pushy, if I can just ask this question again:
Can anyone confirm any major issues I will face in 'P' mode?
Or if I set everything I see in the menus to 'auto' and just change the 'EV' I won't be overlooking anything?
That seems a good place to start, then I will go out later today and put it to the test !