I remember this (although I was going slightly mad between stores at the time).
Thanks for posting the summary - hopefully it will keep people calm

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Three and T-Mobile only share
part of the same network through a company called Arqiva which was set up to erect shared masts for both networks. Not all Three and T-Mobile masts are Arqiva masts. It's a step in the right direction and these shared masts are replacing standalone ones for each network but it is still very far from sharing the same mast network across the UK.
However Orange and T-Mobile share masts through a company called "Everything Everywhere" which if I remember correctly, requires the user to explicitly opt into.
O2 share a few masts with Vodafone and there's always been a little bit of crossover going on although the big mast sharing venture has to be between T-Mobile and Orange which together now make the UK's biggest network. Probably a good choice for reliability given how much their masts overlap each other during the days when they competed in the same areas for coverage.