I think that the House of Lords should be replaced, but not with an elected body. Instead, it should be composed of several different sections.
In theory this could be workable. The biggest problem with this is that all of the other interest groups not covered will want a section, trade unions leap to mind. And if you add them some other group will be next etc etc.
-The first section: retired businessmen voted in by active CEO's. This gives the House of Lords access to knowledge of the Business world, something that far too many MP's lack.
I would modify this. This gives power to big business at the expense of small business. That gives them the chance to push crony capitalist legislation that will further empower the major corporations. "Sure I'll vote in favor for the new defense budget but in return we'll want..." Having a business voice is a good idea since most legislators are lawyers and are a bit clueless as to how business works, but to keep big business from preying on the small, I would split the first section in half. Half of the representatives to be elected by big business CEOs. Half of them to be elected by small business owners.
-The second section: Those who have earned the Victoria or George Cross. Their patriotism is confirmed and those of a military background will have at least an idea of the threats that the country faces.
May need to expand this slightly. As one of the other posters mentioned, there are just too few people who qualify. That said, this would allow the voice of the military to be heard by those who truly understand battle, not just by generals who are more politician than soldier.
-The third section: Those with noble titles as voted for by the nobility. This gives access to those with historical knowledge via family archives and who know the traditions of the country.
Wouldn't work in the US, but I think that it would in the UK. Those from the old system would still have a voice, even if it is reduced. Historically a portion of the aristocracy has served England well by upholding the traditional ideals of noble service, if those happen to be the ones elected....
-The fourth section: Lottery-style selection limited to those who do not have a (serious) criminal record. Petty theft, maybe (as long as it was several years plus in the past) but assault, manslaughter, murder, blackmail, rape etc mean that they are not allowed to enter the lottery. This gives a link to the general populace.
That would be nice. Ordinary people... Definitely a revolutionary concept.
-The fifth (and smallest) section: Former Prime Ministers. Keeps them from trying to covertly sabotage their predecessors and should they try to become Prime Minister again, they'd have to resign from the House of Lords.
Interesting.....
Someone else mentioned Bishops..
I am adamantly opposed to Bishops having temporal power. That leads to individuals choosing to enter the ministry hoping to rise to power, not because they feel called to serve the Lord. Historically those types of individuals have been a disaster for their church(s) and for society at large.
Having a religious component in parliament though isn't necessarily a bad thing. Ministers/priests often have valuable perspectives, but just don't use Bishops. If a religious component is included it should be a lottery of ordained ministers/priests. Similar to the ordinary people lottery. Because it's a lottery, all the backstabbing, behind the scenes manipulations etc which have caused such pain in the past won't work and thus there will be no reason for those of that sort to try to use the ministry to climb to power. They'll try the lower house instead.