The 'unwritten' constitution functions pretty much as is needed. There is no real need for a constitution to be written down, and would simply be a waste of time and possibly money. Not to mention unless the hypothetical written constitution stated that it was the highest form of law and that Parliament could not make any law going against it, Parliament (the highest constitutional power as of current) could just ignore it anyway.
I do not believe a Constitution is in their nature
A stagnated government is a dying government.