Is the current governmental system in the UK (monarchy) working.?

The UK is a constitutional monarchy and therefore the Queen and Royal family are no more then figureheads. The UK is a Parliamentary democracy with universal suffrage, the Queen has no political power (technically she can reject laws but if she did she would be forced to abdicate, the last monarch to reject a law was Queen Anne - reigned 1702-1707, although George III commonly "lost" his papers)