Car insurers will need a physical address where the car is normally kept. So simply using a friend or relative's address when the car is rarely there is actually a breach of your insurance, although some CCer boaters do it.
Official residential moorings are as rare as hens teeth but there are numerous liveaboards who live unofficially in marinas and online moorings. Mooring operators tend to look the other way at such breaches of their terms and conditions, provided you keep your head down and don't disturb them or any floating or land-based neighbours, or draw the attention of the authorities. Some marinas even have a (more expensive) 'high intensity' mooring category which allows you to spend more time aboard while in the marina. A few days away from base periodically is usually enough to show thar you aren't a permanent resident.
Some marinas will allow you to use their address for official purposes (banks, DVLA, Passport etc.), to receive post and courier deliveries, park a car etc. Others won't and you will have to make alternative arrangements.
Don't discount boats elsewhere. You will have a much larger choice. The biggest concentration of brokers is the Braunston/Whilton area. The biggest online boat sales site is apolloduck.com and most of the brokerage firms advertise there as well as private sellers. Browsing the duck will at least give you an idea of current boat prices, but do go and look at a few as well - what appears in adverts isn't always what boats look like in the flesh.