Brexiteers must focus on Parliament, to get what they want.
That’s fundamental to the constitutional democracy they wish to uphold.
The British Constitution is chiefly based on two principles, the Sovereignty of Parliament and the Rule of Law. The former means that Parliament’s will is the law. The latter means that the courts enforce that will over everyone equally. If there is a question about whether any institution – the Crown, devolved or local government, an international organisation – has the power to bypass or overturn a law made by Parliament, the courts have always said ‘No’. Even when EU Law has taken precedence in the U.K., it’s only because Parliament passed a law, the European Communities Act, to make it so. We do not have an absolute monarchy but a constitutional one, so the Crown does not make the law. We are not a direct democracy but a representative one, so a referendum does not make the law. Parliament makes the law.