Welcome to the Forum.
Whilst I'm not based in London, we've plenty of members who are, and I'm sure they'll be along to share their thoughts with you shortly.
And there are quite a few single ladies living on boats, and most will tell that it's as safe as living anywhere, as long as you use common sense, logic and take care - exactly as if you were living in an house.
London has developed a marked overcrowding in some areas of the canal system in recent years, and I'm lead to believe that the CRT (Canal and River Trust) are making efforts to 'police' the system more effectively, and make sure that boats don't overstay at key locations, and that continuous cruisers (those who've chosen not to have a home mooring) follow the rules of their licence.
Boating is much more time intensive than living in a rental flat, it may well take hours to cruise to a sanitary station to empty your toilet, or ti find a tap to fill with water, with a chance that if you then try to return to your last location, there's already another boat there.
And, of course you can live for less than life is currently costing you, but like many things in life there tends to be a direct relationship between physical/material comforts and cost. The same is, of course, true with boating.
And you need to be fairly nifty with electrics, engines, pumps, lead acid batteries and plumbing. Because unlike houses, boat bits insist on breaking down more frequently, and they're dearer to replace too.
We live on our boat, though not in London. And we love it, though working and being a continuous cruiser is possible, I wouldn't fancy it - - though I know of folks who do.
I guess if you have a flexible enough diary to allow for sometimes extended commute times, (and the means to pay for it), and have the time available to make sure you get back to your boat by 5 o'clock in order to run the engine/generator to recharge your batteries, (all engines must be off by 20:00 hrs) - - because your lights/water pump/bilge pump/tv etc need the power.
It IS doable Pennywise, but it may well require a number of major changes in your lifestyle - - and they're not all easy ones.