It is actually misleading to call the UK constitution unwritten. Rather it is whole libraries of writing. Instead of a single document we have centuries of documents - acts of parliament, decisions of courts, treaties. In the margins we do have issues around parliamentary conventions (which in theory could be breached) and we do have the royal prerogative (use of which has in the past prompted revolutions). The bedrock concept is that of the sovereignty of parliament, which means that parliament is the ultimate authority.
The constitution is evolving to take account of devolution and it is evolving in its relationship with EU law. In EU law we have the concept of subsidiarity where a decision in the courts of any EU country applies in all EU countries - and in this respect parliament appears not to be the ultimate authority.
The present government may well have to look at some of these issues.