Difficult to know what to advise without knowing more about you & your parents' desired lifestyles.
If they are say early 60s, no ties, fit and healthy, and enjoy a 'basic' lifestyle (like say bush camping) and want to spend 10 years really travelling around the UK canal and river network then get a narrowboat and go for it. Continuously cruise all summer and perhaps look for a marina mooring each winter (stoppages, poor weather, short daylight hours, more challenging electricity management etc). But keep enough in reserve for maintenance and for moving onto land in say 10 years' time.
As others have said, not sure I would recommend a permanent marina mooring for them. If they want to be fixed somewhere, then better options might be a house in a cheaper area of the country, or if not affordable a (mobile caravan) park home, which may have similar residential restrictions but at least has a permanent water supply, plumbing and electrics.
For the London show, bear in mind that many canal dwellers in London are what are often referred to here as 'continuous moorers'. They have a continuous cruising licence, but for either work or family reasons don't really want to move, so they aim to get away with the minimum that doesn't breach the licence terms. With London canals also being quite crowded, this can mean periodic 'moving days' every few weeks, where everyone simply shuffles around swapping locations. This doesn't really compare at all with 'true' continuous cruising away from cities, where you can moor almost anywhere you like, moving on around the network as required; simply stop for water, fuel and waste disposal as needed; and visit many interesting places around the network.