A letter in today's Daily Telegraph sums up the dilemma succinctly:
"SIR – Some have suggested that everyone in the United Kingdom should have a vote on Scottish independence. I don’t fancy having to deal with a similar argument when we have had enough of the EU.What follows is purely conjecture, however were Scotland to vote for full independence and left the United Kingdom, what would the remainder of the present United Kingdom be called? It can't be given the name Britain as that is England, Scotland and Wales and it will be recalled the full name of the United Kingdom is United Kingdom of Great Britain and Northern Ireland.
Also consider, if Scotland were to subsequently apply for membership of the European Union, it would have to accept the euro as its currency and would also be forced to accept membership of the Schengen area. Because of this - and I believe I am correct - it would then be necessary for England to set up external border and passport checks at the new frontier.