The United Kingdom has no written constitution!
What currently serves as the constitution of the United Kingdom of Great Britain and Northern Ireland is merely an aggregation of the laws and principles that make up the body polity of the United Kingdom, these laws and principles governs the relationships between the citizens and the state, how the legislature function and the powers the judiciary and the executive arms of the government.
This type of constitution is called an “uncodified” constitution and is not peculiar to the United Kingdom alone. New Zealand, Saudi Arabia and Isreal have no codified constitution either.
Absence of a written constitution for the UK meant prior to 1972 that the Parliament was the supreme law-making body in contrast to nations like the United States of America whose laws must conform to the constitution. This gave the Parliament powers to make and unmake laws making the constitution very flexible.
After 1972, which was when the UK joined the European Union, EU laws took precedence over British laws whenever the two conflicted. If the Brexit is triggered, this is one of the issues that would need be sorted out though the Parliament in 2015 had come up with a draft written constitution which took 5 years to come up with.
The Draft constitution in pdf format is here .