It being undemocratic is actually pretty important for the system to work.

Because only the house of commons is elected they have legitimacy and the house of lords knows that while they can resist some dumb crap, they do ultimately have to accept the decisions made there.

If you have two elected houses you end up like the US with the senate blocking everything the house of representative does.

A more representative second house with less rich people and politicial cronies would be nice though.