The only issue with codifying is that to do what you wanted would require an English constitution, with Scotland having to pass its own. The alternative is backtracking slightly on devolution, British Parliament requiring devolved nations to comply with a centrally imposed requirement (such as education provision). Tuition fees is an interesting example as for some time Scottish and English legislation differed greatly, with the latter imposing tuition fees not found in the former.

I would however like to see greater use of referenda, and greater devolution.

I think the example of the control orders is one that shows the effectiveness of the safeguards in our system.

The advantage to codification, in my view, is that it sets rights in stone, hindering any possible attempt to do away with universal healthcare, education, etc. If referenda were required to alter the constitution, it would make it harder for a future Tory government to undo the progressive achievements like the minimum wage, devolution, and so on.