Whatever will be left of the UK will have to accept that it is no longer an EU state and will not maintain the same access to the single market that EU states have. That is reasonable.
That will be England, Northern Ireland, Scotland, Wales, IoM and the Channel Islands then, just as it is now. They can always fund their own referendum out of the taxes they raise themselves to see what the people want, and then put it to Westminster to see if parliament accepts it. THis would mean a complete severing of all ties and visa's, passports and I.D. cards being needed to enter the UK. No £ anymore so they will have to create a new currency, then find employment for all the people currently employed by British government in places like Faslane and Nuclear energy plants.
Once again you jump inwithout first thinking it through what the prospects are of slitting the Union