Everyone loves an intermittent fault!
1. Have we confirmed it is the power supply at fault, and not the television? Does the television behave when plugged in elsewhere? Have you tried not turning the television off overnight? (Mute the sound, so you can sleep, obviously). It could be a dry joint or some other fault on the TV which only manifests when it is cold.
2. Do you have a dairy farm near you? The neighbour's milking parlour power consumption plays havoc with my mother's power supply - might be the same thing, especially as it is early am. Could also be the local iron foundry or other factory process (just because you have Devon in your screen name, I have an image of green fields and pastural idyl, but you could live in Swilly for all I know).
3. I have an LG flat screen TV of quite elderly provenance, which started randomly turning itself off. A quick YouTube search for the fault suggested dust was a problem: I whipped the back off, and blew most of the Sahara out of the thing with compressed air, and it has worked perfectly ever since. Not suggesting this is your problem per se, but it might be a particular known fault for your model, that other people have found a solution for.
I don't know if any of the above is of help, but fingers crossed. Oh, and if you get an electrician in, he may immediately want to replace your consumer unit, not because there is anything wrong with it, but because it is a big ticket item.