This issue must have been confronted at some point by the travelling community. I can't imagine that all members of that community are self employed and don't have bank accounts, etc. Also, within that section of society there's no shortage of quality vehicles costing a small fortune that must be insured and taxed somehow. And benefits can be accessed so some mechanism must be in place.
Perhaps one of the traveller's support groups could give some guidance here?
On a philosophical note, I lament the loss of a freedom in this country, that of anonymity. Ooops, sorry, I'll move into the pub!
Good luck whatever happens, your wait for a mooring might not be as long as you might think, sometimes these things move very quickly.