There's tonnes of evidence that proportional representation and voting systems other than FPTP are important for the health of a democracy. The problem in the UK is that the parties in a position to make it happen stand to lose a lot of power as a result, so it's not likely to happen.

The 2011 Alternative Vote referendum was a solid victory for FPTP, and it's often used as a cudgel on anyone who dares to suggest a better voting system.