As I've said elsewhere, a second elected chamber is not a good idea if you belive in the authority of parliament. Because although in theory, and probably also in practice, the Commons would still be pre-eminent, whenever there was something particularly controversial like the Brexit Bill hoo-ha, the fact that the Upper House was elected would give it an authority or an authenticity which it probably doesn't merit and would not be good for legislation.
Better an appointed - but smaller - body which, as now, has the role of debating and suggesting amendments to Commons Bills, without, as someone said above, needing to be concerned with the electoral cycle. Maybe a third of them could be elected. The trouble is you end up with endless elections: we already have quite a lot as it is. And we all hate our elected representative don't we?