It doesn't have a codified constitution in the US sense but it does have a constitution:
https://en.wikipedia.org/wiki/Constitution_of_the_United_Kin...
Edit: I would certainly agree that having constitution in this form isn't a great idea...
https://en.wikipedia.org/wiki/Constitution_of_the_United_Kin...
Edit: I would certainly agree that having constitution in this form isn't a great idea...