If you were to give take a broad guess at the cost of moving around like that, in terms of maintaining supplies and securing a place to stay when you’re not in the mood to move with the current, what would that come out to, say monthly?
Boat pricing comes in a spectrum that very roughly looks like this:
3. £20-£40K Narrowboats are thirty or more years old, or are under 50ft. They have had many owners each of which will have done something to the boat. The engine fittings will be old eg. coolant hoses , the radiators might not work, the fireplace might need replacing, there is rust in important places needing welding and so on. There may be overplating on the hull to repair holes. In general, you can expect to perform regular/constant maintenance and repairs to maintain and keep them in working order. (some people enjoy this, you may not)
4. In the 40-60K range expect the boat to be about 20 years old. Generally modern and most things will be working but it might not have a good electrical system for modern lifestyles. It will have 20 years of wear and tear, and the interior might feel old and outdated.
5. In the £100k-£120 range you should see 5-10 year old boats. It probably will have a modern toilet/shower, modern electrical maybe a solar panel, a nicer kitchen and modern diesel engine/gearbox and propeller.
6. At £160K-180K you can get a new but simple/basic boat fitout probably no solar, no dinette, few cupboards. Or it’s a five year old custom build that has been fully fitted with many extras e.g washing machines, quality inverter/batteries
7. At £200K+ it a brand new boat, built to your specification. An all electric boutique boat is £220K-240K. I’ve heard of narrowboats up to £280K. Luxury wide beams over £350K do exist.
Edit: You wanted a figure - for the sort of boat you'll find on a canal in the UK. Bottom end: buy a small fibreglass boat for £5k, pay £1k a year for your licence (many at this end don't bother. Another £1k a year for maintenance and fuel )
Top end: Buy a big boat for £300k, £2k a year licence, £6k mooring, £1k insurance, £5-10k a year in maintenance.
Also factor in that boats mostly depreciate (though the last couple of years have been an exception). If you spend £100k on a boat today, you won't be able to sell it in 10 years get that £100k back. If you fail to keep on top of maintenance a boat will rapidly lose value.
A few grand a year for a mooring, plus around £1k/year for your license (all boats on the Canal and River Trust's waterways must be licensed). Every few years you need your boat lifting out and the blacking on the bottom re-done (more £££), and in winter you get through a fair amount of coal and other fuel to keep the boat heated (I think we're at about £100/mo for diesel + coal, but some people burn a lot more coal than us).
You really have to want to do it for the experience of living on the canals rather than a way to live cheaply (though it can be done).
You can do it for almost zero money (perhaps $100/month) if you put many hours per day into maintaining the boat yourself and making everything you need yourself.
Or you can pay for good gear and get all maintenance done by a professional and your canal boat will be costing more like $3000/month - and when you do that, it becomes a rich persons hobby.