Britain, almost uniquely amongst mature democracies, does not have a written constitution. Constitutional practice is uncodified and evolves by precedent and convention. Formally, absolute sovereignty remains with the Crown in parliament and although this constitutional myth remains intact, it is wearing increasingly thin in the era of an enlarged European Union. It follows therefore that referendums can have no formal status under the British constitution, but even so their usage is not proscribed, and their occasional usage in the future appears probable.
Balsom, D. (1996). The United Kingdom: constitutional pragmatism and the adoption of the referendum. In The Referendum Experience in Europe (pp. 209–225). Palgrave Macmillan UK. https://doi.org/10.1007/978-1-349-24796-7_13