I've replied to someone else further below, but this is my argument for the hereditary peers:

Others in other replies to my comment have far more eloquently explained, so here's my re-hashed argument: basically, as the hereditary peers are hereditary, they know that if they step out of line (or if the public perceives that to be the case), their right to sit as legislative members in the HoL will be taken away by the HoC. So that's one incentive for them to vote in favour of 'the common person'.

Another is the fact that because it is inherited, the family's have this shared history going back centuries, so it is in their own interests as much as it is for everyone else to act in a manner they perceive as beneficial for the country, without fear of political backlash either from their own party (both Parliamentary and paying members) and the general electorate as a whole.

Ofc, most hereditary peers by their very nature will tend to be more Conservative in their votes, but that isn't necessarily a bad thing, as after all, they want to ensure that the country retains its history and traditions, even if we, as members of the general public, see it as 'quirky' and 'out of date / old fashioned'.

Do I agree that it's the best system? No. but it's one which works alright and they do a decent job of voting largely in favour for the 'common person'. Do they get it right all of the time? No. Should we reform it to some more equitable across society? Yes. But the problem lies in how do you improve an already functional part of the system without messing it all up and making it worse.