Parking is not a problem, but no way am I driving into central London in rush hour.
Brings back memories of a long holiday many years ago. I bought a combi in Holland, complete with anti nuclear stickers all over it, and a rather scary looking LPG conversion (I was too scared to try it).
Came over to the UK by ferry, with my evil ex push starting it at every stop as the battery was dead. (She was evil so I have no sympathy). I drove it around for months without insurance, MOT or tax because I didn't know what was supposed to be needed. It wouldn't have made much difference anyway as I didn't actually have a driver's licence for a car, just a motorcycle.
Fun times. Especially camping in the Lake District in the middle of winter with icicles descending from the roof.