My commute home was very similar to that into work, insofar as the half nearer to the centre of town was almost entirely snow free, whereas the half on the Croydon side had the remnants of snow on the footpaths, and some roads.
Around Norbury I use a small section of shared use path, which crosses between two no-through roads. One of these roads was scary, the snow had been compressed into a sheet of ice that was difficult to stand on. Having seen that, and knowing some of the roads nearer home would have had a similar level of traffic, I took the alternative route via the Purley Way, which I normally avoid on the grounds that two of the junctions are lethal.
It wasn't until I got to my own road, which is similarly no-through, that I had to get off and walk again. Just turning into the road I could see the sheen of the ice, so didn't even attempt to cycle on it.
I think the temperature around London must be hovering around zero, so once you get outside the heat island effect, it drops a degree or two, and everything freezes.
I don't think I saw any bikes on that trip, but at this time of night, it's not unusual to see none.