It's not too late... Britain must vote again
In the Irish and British parliamentary tradition, making binding law is taken so seriously that it must go through two houses of parliament and a number of stages in each before the die is cast. This is the democratic due process.
Ireland has a written Constitution; this is the basic law of the State and to change the Constitution, the Houses of the Oireachtas must pass a Bill, which, unlike normal legislation, cannot be referred to the Supreme Court by the President. The Bill goes directly to the people, who vote on it as the ultimate legislators in this type of law. If the people reject a proposed constitutional amendment, the Oireachtas may try to assess the real concerns of the people and, as they are authorised by the people to do under the Constitution, put the question to the people again.
This happened with, for example, divorce proposals and two EU referenda (Nice and Lisbon).