The short answer
The UK does have a constitution, but it is uncodified, which means it is not written down in a single document. Most democracies have one master text you can hold in your hand. Britain's rules are spread across many places, and most of them can be changed like any other law.
Where the constitution actually lives
It rests on four main sources. Acts of Parliament, from the surviving clauses of Magna Carta to the Human Rights Act. The common law built up by judges over centuries. Constitutional conventions, the unwritten rules that everyone follows without a statute forcing them. And the works of authority written by figures like Dicey and Bagehot, whose account of the constitution is set out on the English constitution page.
Uncodified, not unwritten
The common shorthand is unwritten, but that is misleading. Most of the constitution is written down, in thousands of pages of statute and case law. What it lacks is codification, a single higher-law document that sits above ordinary legislation and is harder to change.
Why it matters here
Because nothing is entrenched, a simple majority in Parliament can change the constitution itself. That is how the settlement after 1997 was built, and it is why it could in principle be reversed. This flexibility is the whole battleground of the Starkey Thesis, and it is the difference between the political constitution and the legal constitution.