The British would be wise to find a way to finesse the issue. This could be done by establishing Northern Ireland as a special customs zone, permitting free trade and movement with the Irish Republic but re-establishing customs and immigration barriers between Northern Ireland and the rest of Britain.
That is the only solution.
However, in may 2017 Theresa had an unnecessary election in which she lost the Tory majority and had to get into a coalition with the northern Irish party the DUP which opposes what you described.
Since then, everything is stuck. Thanks to the DUP