But wheres the job?
Whilst there a two docks adjacent to the City in E London, it just might be easier / cheaper to berth away from the City further south (like Chatham or on Meday River) and commute via regular rail into central London?
An invaluable resource would be Jack Tyler's report on his winter aboard in London - see the website John's Sailing Web - which is hosted by John Stevenson. Look for the part about S/V Whoosh, which is Jack's boat. He has a ton of great info about European cruising generally - the best I have seen. John on S/V Sarah has also been cruising Europe and both of them have lots of great ideas.