The house of lords had major reform at the start of Labour's last stint in government to remove hereditary peers. It's not impossible to go further, in fact I'd put it at about the same likelihood as reforming the EU structure in the medium to long term.

Besides, short of violent revolution there's nothing the UK population can immediately do about the HoL. The Brexit vote was something that the people could directly do to at least de-abstract power and bring it closer to home. This was one of the most-advertised perks of the EU by the remain campaign: It's not the same as a nation superstate because you're able to voluntarily leave. Brexit was just the UK population exercising that right.

The other point is that the Lords really doesn't have that much power when all's said and done. Yes, they can quibble and send bills back for review a few times, but they're nothing like the US senate for example, the commons have the final say over everyone else. Compare to the EU commission, who have much more power, and actually make the laws.