Looking at the #uksnow map, there's a little bit in the middle of the country, but nothing getting anywhere significantly close to That London. Even if any snow does come this way, the temperature's going to have to drop a bit before it'll do anything significant. Currently with London City Airport at 0°C, and Biggin Hill barely below zero at -0.6°C, I can't imagine much will happen.
I guess tomorrow could be a bit different, and the forecasts suggest there could be a bit of snow, but probably not until middayish.