Lord Hylton
Most on the left dont have much time for the Unelected House of Lords and former Labour leader Tony Blair was one. He has never accepted a peerage. He may be disliked for other reasons but his decision to remain an ordinary citizen, albeit a very wealthy one, reflects a long standing New Labour principle.
The detail of attempts to reform the Lords is below. Labour’s 1999 Act managed to significantly reduce the number of hereditary peers and increase the focus on life peers. Subsquent efforts under Labour to scrap the remaining hereditary peers failed.
After 2010 the modern Conservatism of Cameron and Clegg, following on from Blair, planned to quite considerably curb the power of the Lords. That too got nowhere.
Blair’s plan to elect an element of the second chamber, like several other of his better instincts, also failed to happen, and after this efforts to democratise the place further were replaced by other much less happy objectives elsewhere.
Changing or abolishing the Lords as Parliamentary history back to the Parliament Act of 1911 underlines is no easy matter
https://en.wikipedia.org/wiki/House_of_Lords_Act_1999
Didn’t Blair change his mind about an elected second chamber after he’d started the process of reforming the Lords?