Something to consider with London is that 37% of the people who live here were not born here, so may well not be eligible to vote, unless they've married a Brit and have become nationalised. None of the immigrants I know, for instance, are eligible. Of course, they may all have voted Labour anyway, but it's worth remembering.
I think you're selling things a bit short here by focusing purely on economics, for there is also a disconnect between who should be providing the service. The left seem to believe that the state is not only the best group of people to provide a service, but should be the only group of people to provide a service, which is just as elitist as this notion of 'trickle down'.
It's also increasingly out of step with the modern world. There's a saying in innovation circles - "whoever you work for, the smartest people will work for someone else". In other words, it's madness to assume that only you have the answers to a particular challenge, because it's inevitable that if you open up your thinking, and increasingly your service, there are better options out there.
Take, for example, the most rapidly expanding technology the world has ever seen - the smartphone (most of which are powered by
UK brains incidentally). I'm not going to sell the hardware short, because the average smartphone is a wonderful bit of kit, without a shadow of doubt. The real value in the smartphone however comes from the apps that are created for it.
Whilst there are some apps that are produced by Apple and Samsung, Google and Microsoft, the vast majority are not. Millions of people from around the world have developed add-on services to turn what is a useful bit of hardware into the most versatile device known to man. The modern smartphone can do everything from conduct medical procedures to monitor air pollution, all because of the ingenuity of people that have nothing to do with the manufacturers themselves.
So, if you look at the 5 Year Plan for the NHS (which predictably barely any of them referred to when scaremongering about privatisation), that is exactly what they're talking about. It's admitting that government doesn't have all of the answers, and shouldn't claim to, and that by opening up the process, it will almost certainly produce better services for less money.