In London, gas is nearer £30 per bottle, and diesel much more than a pound if used for propulsion.
Boat economics are rather different from house economics, and costs can be much higher if more than basic maintenance is required. Hence the importance of a thorough survey. And if you view a boat as a cheap alternative to owning a house, you will be disappointed (renting is a different matter). There are much better reasons to live on a boat than saving money.
You will find it easier and more pleasant and not necessarily hugely more expensive (if your boat is well insulated) to heat electrically if you are on the mains. Coal is dirty stuff, and diesel can be smelly.
If you're ever in West London you are welcome to view my boat, which is a barge, and in my view it has several advantages over a WBNB (it will still manage the broad canals). Mine is a bit of a floating building site at present, but that should prompt a few questions.
With a barge, you also have the option of exploring the Medway, the Essex rivers and creeks, and popping over to France. So the cruising ground is not as restricted as the Narrow-boatists would have you believe. It's not just the beam that is broader, it is the horizons too. Whilst I accept that you CAN cross the Channel in a NB (or even a WBNB), it is not the craft of choice.
That said, there are many absolutely delightful small canals, and I am glad I have done a bit of NB hiring in the past.
Good luck.