Personally, unless you can fit long distance travelling into your work life (i.e. a cruising range from, say, Uxbridge right up the Lea), find a more suitable boat (i.e. a 40' narrowboat) and don't mind spending every weekend sorting out boat things (getting water, pumping out etc etc), I wouldn't recommend CCing. Also, are you fairly good at DIY? If you can't fix most engine, electrical and plumbing issues yourself, you can end up spending a lot of money sorting out little problems.
From time to time residential (and even leisure moorings that allow casual living aboard) come up in London, but the affordable ones aren't near your work. Still might be worth considering though, and worth bearing in mind if you chose to move jobs.
I completely sympathise with the need to find affordable accommodation in London. I also know how brilliant it is living on boats in London - waaay friendlier and more fun than flat sharing. It is, however, fairly difficult to manage these days. Think carefully
Good luck, and welcome to the forum,
Lucy