In her case, baroness is the title she got when appointed to that house. She isn't a hereditary baroness, which still exist.
The real problem with the House of Lords is that it's packed with political appointees - like Meyer - and quite a few were appointed after losing their elected position in disgrace.
A majority of people want away with it, just not the people in power. A law getting rid of the house of lords would have to go through, you guessed it, the house of lords.
eh, every time there's a referendum it gets plurality of support. A bunch of people like the pomp and circumstance. And although I disagre I can understand.