It might work for the UK, but the UK is quite different from the US. For one, the house of lords was supposed to represent the wealthy whereas the Senate is supposed to represent the states.
Secondly, there are far greater geographic distances and differences between the members of the country. This usually means there are great differences in needs and priorities. This was kind of the point of reserving most rights for the states. If using simple majority, the smaller and more rural states will eventually get tired of things being crammed down their throats. We are starting to see this already with an increasing number of sanctuary city/states and multiple topics.
Lastly, does it actually work well? It seems that almost 2/3rds of people in the UK think the rural areas are neglected.
http://www.thecommentator.com/article/7587/government_neglec...
I assume you're talking -- primarily -- about the Senate and the filibuster? If so, you'll be pleased to hear the UK has managed OK for the last 400-500 years in having a parliament that can do _literally anything_ it wants with a majority of 1 person[0] including deciding to pick on a single person individually without trial and subject them to whatever it pleases[1].
[0] https://en.wikipedia.org/wiki/Parliamentary_sovereignty
[1] https://en.wikipedia.org/wiki/Bill_of_attainder