The majority of modern canal boats are diesel-powered. Even electrically-propelled ones tend to have a diesel generator on board as well as lots of solar panels since there’s insufficient sun in the UK to support year-round solar-only propulsion.
However, unless you set out to cruise for several hours each day, every day, the amounts of diesel the boats use is relatively tiny. Consider that a good estimate for consumption is between 1 and 1.5 litres per hour; in four hours of cruising that’s 4 – 6 litres.
But then you might well stay in one location for several days before moving again, and only use diesel briefly to heat water for your shower perhaps (either via the engine or a dedicated heater).
Thus notwithstanding the astronomical price of fuel these days, the cost need not be too horrific unless you really are dead-set on seeing every inch of every canal as quickly as possible. That will also apply to petrol-run outboard motors as well of course.
For diesel, there’s a crucial tax issue to be aware of though. When purchasing diesel fuel for boating, it is taxed at two rates, one for domestic use (eg heating, hot water) and one for propulsion. Crucially, the domestic rate is substantially lower than propulsion.
However, canal boats tend only to have a single fuel tank so any purchase must have a corresponding declaration for tax – by you – of how much fuel is used for each purpose. Oddly, this system relies on trust between the taxman and the boater (yes, it’s very peculiar)
Legally speaking, it’s you who dictates the split (ignore any marina that insists on a set amount, it’s you that’s liable, not them) but in reality His Majesty’s Inland Revenue Service has stated since 2008 that a 60-40 split is likely to be accepted without question. That’s 60% propulsion on the higher tax rate, and 40% domestic on the lower.
Some canal boats may have a dedicated tank for diesel used for heating as would any cruisers with petrol motors for propulsion but a diesel heater installed. That dedicated tank can be filled at 100% the domestic rate.
Fuel is supplied as ‘red’ diesel which is merely standard diesel with a red dye applied, there’s nothing magic about it.
Back in 2020-2021 there was a Government consultation about banning the use of red diesel altogether which would have meant fuel suppliers and boaters fully cleaning out their tanks to remove any red, before then going on to use white (with the same tax split so really a very costly and pointless exercise) but in the end the outcome was that pleasure boat users in Britain can continue to use red diesel, and split the taxation as before.
What’s not taken account of in the rules yet is how to split fuel used in a generator to charge batteries (which, on an electrically-driven narrowboat, may then be used for domestic or propulsion purposes) but it is my personal expectation that the 60-40 rule would still apply unless you can show evidence to the contrary to HMRC if you’re challenged.
 See https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/966132/Summary_of_responses_to_the_red_diesel_consultation.pdf and https://www.gov.uk/guidance/fuel-used-in-private-pleasure-craft-and-for-private-pleasure-flying-excise-notice-554