I am obviously painting a best case scenario!
But one which, given the right leadership, is possible. Cities have dealt with plague and mass deaths before, they usually survive, I don't think it will be the bodies or the shit that will be the problem. The thing that humans eventually realise whether they are in a city or the country is that we actually need to work together for any of us to survive. Either that or they dissolve into civil war killing everyone within a short space of time. But the world-wide evidence is that that happens very rarely. I do think it will probably become distinct local areas under a local leader (leader, probably elected, not Mad Max style warlords) simply because co-ordinating an area as large as Greater London under one administration would be very difficult in those circumstances. Assuming enough food can be grown, which, if there has been a significant death rate there will be enough space for, I actually think the biggest threat will be fire. Most people are not used to dealing with real flames. I think there will be a lot of accidental fires which, without a co-ordinated fire service will destroy large areas and with them lives, crops, solar panels and stores.
I think it is very easy for fiction writers to portray piles of bodies, rubbish and rubble as the only future for cities, but I'm not so sure. One scene in Threads (1984) in particular brought it home to me: 20 years after the bomb, people are going in and out of a house that is clearly being used as a pub, climbing over rubble from the collapsed neighbouring building to get to the door. I cannot believe that in 20 years no-one thought to themselves "Ya know what? I'm tired of nearly breaking my ankle just to get me a pint of an evening, I'll just shift these bricks to the side leaving a nice clear path. One morning's work tops." I just don't think people will live like that. It doesn't make sense.