Can you ask your family about using their address for all your legal stuff?
(it's useful to have bank account, insurance, car registration and driver's licence etc all at same address)
I lived in a truck for years, and moved around a lot - so was 'no fixed abode' for doctors etc. Both my vehicle and my driver's licence were registered to my parents' house for over a decade - not a problem at all for the DVLC. Please ignore all the people telling you it's an offence that you'll be fined for! As long as any correspondance goes somewhere safe, where it will reach you, that's enough. If your family's address is stable, and you think it's unlikely to change any time soon, use it! Better to do that than rely on (and pay for) Royal Mail redirection services for any length of time.
Your bank and most others will be very happy to communicate with you via email most of the time anyway.
If you're planning to get rid of the car anyway, then yes, look into cheap vans (or estate cars - something long enough to lie down). If you have a tow bar, another cheap option might be to buy an old touring caravan. Do you know of anyone who would maybe let you park this in their driveway/ garden, and provide an extension cable, in exchange for a small amount of £?
The good thing about being in a tourist town is that there are probably loads of locall businesses (incl all those air bnb owners, cafes, pubs etc) that struggle to find staff, as nobody can afford to live locally. If your new dream job isn't too onerous/ inflexible, could you combine it with - for example- doing changeovers in an air bnb? This would mean being around on Saturdays to do all the cleaning, change the beds etc - perhaps you could negotiate for a parking spot plus pay for this?
Would echo what others have said about checking out WWOOF and HelpX, also about looking for pet-sitting gigs over the summer holidays (if you like animals) and seeing if there are any elderly people who would appreciate having a live-in helper and offer you a room rent-free in return for some simple tasks (shopping, basic care, light housework).
When does your new job start? Once you're there, you might feel more able to confide in one or two of them (in confidence) about your situation, and they might well be able to help in some way.
Good luck!