Unless they can get Dublin to join in, then it is easy (if costly) to circumvent by taking the ferry to Northern Ireland, and then crossing the land border to Ireland.
1) You need to notify the Border Agency when you are travelling between NI and GB, which is easy to police, but would anger the Unionists,
2) You need to notify the Border Agency when you cross the between NI and Ireland. This is almost impossible to police. Infact, on the smaller roads, the only way to tell that you've crossed is that the road signs are a different style and are in km not miles.
I seem to remember that the government were proposing option 1 in this, or a similar bill.
Non-EU visitors crossing the border are meant to notify the Police/Garda each time they cross , but I doubt that many people do.