As far as I am aware there is no written constitution for the UK but we do have all of our statute law and the interpretations created by courts via 'case law' and also we now have the effects of being in the EU and the UN and ratifying things like the convention on Human Rights which is so beloved of some who post on AB.
Example - there is no statutory constitutional 'right to life' as is the case in the US of A but we do have a law that makes murder illegal.
That is a very simplistic explanation, the reality is more complex.