London, April 14 -- As a symbol of the woes of Britain's Brexit-era democracy, it could hardly be bettered. Lawmakers had to be sent home in mid-debate last week when water from a burst pipe began gushing into the House of Commons chamber.

The image perfectly illustrates Parliament's problem as it tries to solve the puzzle that is Brexit. On the outside, the U.K. institution is resplendent, a world-famous symbol of democracy sitting majestically on the River Thames. On the inside, it's decrepit and increasingly unfit for use.

The hidden flaws in Britain's political system have been laid bare - and televised worldwide - since voters chose, almost three years ago, to leave the European Union.

Decision-making has ground to a standstill, e...