As dsfyu404ed@ points out, the UK no longer has good track-record of due process and fundamental-rights compared to the continent.

In 18th and even 19th century, Britain's unwritten constitution and notions of "English liberty" did indeed stand out -- and inspired the American to crystalise the ideas into written constitutions.

But 20th century ideologies, and the modern administrative state have "obsoleted" all that. Needless to say Britain coped with the change better than lots of pre-war countries (Germany!).

But post-war, Europeans have put in place formal human rights protections that a working imperfectly, but better than the British non-constitution. British citizens have their basic rights protected in large part because the UK now shares these formal rules with Europe.