It's made up of different laws and so on. There's nothing stopping anyone writing it all down on a single piece of paper, if you just want to record it all like that (although you'll probably need some legal scholarship to decide what is and is not "constitution"), on a single piece of paper. But it wouldn't hold any particular force.
I suppose if you wanted to make one new legally binding document making up the constitution, the UK could cancel all those laws, recreate the bits of them that make up the constitution in one single place, and then make new laws to fill in all the gaps from all the cancelled bits that weren't part of the constitution. Some of the UK constitution is procedure and books of commentary and theory, so those are going to be awkward to rewrite and put on a single piece of paper, but it could be done.
I suppose if you wanted to make one new legally binding document making up the constitution, the UK could cancel all those laws, recreate the bits of them that make up the constitution in one single place, and then make new laws to fill in all the gaps from all the cancelled bits that weren't part of the constitution. Some of the UK constitution is procedure and books of commentary and theory, so those are going to be awkward to rewrite and put on a single piece of paper, but it could be done.
But why?