Earlier quoted context omitted.
We already have a constitution. It just isn't a written constitution: > The United Kingdom constitution is composed of the laws and rules that create the institutions of the state, regulate the relationships between those institutions, or regulate the relationship between the state and the individual. These laws and rules are not codified in a single, written document. Source for that quote is parliamentary: https://…
Right of course every state has a "constitution" but the contemporary connotation of the word means an enforceable law that meaningfully constrains the state's power.
Just because it isn't 1 document like in the US, it doesn't mean it's not a constitution.
I think what you mean by "contemporary connotation" with "American connotation".