One perpetual complain in British politics relates to the undemocratic nature of the House of Lords. This House has very considerable power within our supposed democracy, and yet its members are mostly appointees of the Prime Minister. Surely it ought to be reformed so as to genuinely reflect the will of the people?
The counterpoint to this is that the House currently plays an important role of review. Very few current members inherited their positions; rather, they were appointed on account of their expertise in particular topics important to our politics. Making them elected would turn them into simply a body of puppets of the party leaders.
Here's a suggestion for how we might attempt to combine these concerns: make the House of Lords into an epistocracy. Maintain universal suffrage for the House of Commons, but also introduce a test which one must pass in order to gain the right to vote for the membership of the House of Lords. The questions would be a mixture of reading comprehension, numeracy, and factual knowledge about a range of topics (geography, the nature of the British constitution, uncontroversial things from economics - comparative advantage, definitions of various things, the current UK GDP per capita). In order to vote, you would have to achieve a particular score - say, 70%. In order to stand for election to the upper house, you would have to achieve an even tougher score - say, 90%*. Upon taking the test you would be informed if you had passed to a sufficient level to vote or stand for election, and if you had then you would receive a right which would need to be renewed every five years.
Every citizen would be entitled to take this test, free of charge.
* Alternatively, perhaps we might say that in order to vote one would have to be in the highest-scoring 10%, and in order to stand one would have to be in the highest-scoring 2%. I'm not committed to any particular formulation of this idea, I'm just throwing it out there.