Fascinating. Can you explain why southern London is DC while northern London is AC?

Prior to 1948 when they were all nationalized into British Rail, there were various railroad companies operating across the country. One of these was the Southern Railway, which, well, operated in the South. They started electrifying very aggressively in the mid 1920's. At the time most of what little electrification there was was in London on the Underground.

Compared to AC, 3rd Rail DC is cheaper to install, especially as a retrofit (Overhead wires require bigger tunnels, and increased spacing around tracks for the masts). Downside is that it's not really great for speeds above about 60-70mph, as well as being a bit of a pedestrian hazard. (Ever the one about not peeing on the rails so you don't get shocked? That's 3rd rail DC.)

For the Southern, with it's mostly short routes with many stops, electricfiation was a pretty obvious win, and doing 3rd rail made sense because they could do it quickly and cheaply.

In contrast, the northern routes were electrified muuuch later, after steam had gone away. The main East Coast Mainline from London up to Newscastle and on to Edinburgh wasn't fully electrified until 1991. By the '60s and '70s, with train speeds increasing to 80mph and up, overhead AC was the clear winner.

If you look closely there are a few exceptions - the Merseyrail network in Liverpool is DC. Built 1970s, but using some existing underwater tunnels, and slow speed commuter. Then running ESE from London you have the high speed AC lines leading to the Channel tunnel. Well spotted, the trend generally is quite distinct.