Yes, in all of Greater London you might have a whole 5 - 10 survivors. They could probably meet up if they put their minds to it and didn’t just look at the desolation around them, reasonably assume they were each of them the last human being alive, and hang themselves to get it over with.
Greater London’s a big area to cover unless you actually think there might be some point in looking or devising a means to communicate with anyone within 20-odd miles. There are ways, but you have to start out by thinking there’s even a possibility of finding someone.
Other major cities in the UK might have one or two people apiece, ditto on average for each of the forty-odd counties.
I’m unfamiliar with the show mentioned, does this premise leave technology/infrastructure intact in the immediate aftermath (it’ll degrade over time - some quickly, some slowly)? If so, then could a survivor go to a radio station and try to figure out to broadcast a meeting place for survivors within the listening area? It’s risky - telling people where you are - but if I was completely alone, I’d probably take the risk. But I’d have no idea how to use the equipment at all, much less set a loop so that I didn’t have to repeat myself over and over again.
Read “Dies the Fire” … Stirling covers it pretty well.
Also read “The Nantucket Trilogy”
Stirling does covers it pretty well. Read both of them. But scenario here is somewhat different. Here deus ex machina just simply decimates (milionites) population to powder (if I understand OP correctly). So we have random 7000 intact survivors scattered around the world. Definitely Stirling material, but for us amateurs to work on. 
I was thinking “Earth Abides.” I don’t remember what the exact death rate was from that plague, but it was, I thought, a pretty realistic depiction of how society would recover from a severe die-off. Isolated pockets of humanity survived and began to form tribes. Travel was very difficult so they began to evolve different customs – the world became a much bigger place. By the time the central character is an old man, his people are living at a sort of pre-colombian native american level technologically, and he notes how the language had begun to change from what he remembered of the old society.