Obviously Bercow is an idiot, and this is already being sorted.
The HOL was culled in the 1999s with the abolition of the Life Peers. By then it had bloated to 1300 members, largely due the Thatcher and Major dishing out Peerages like confetti to gerrymander the second chamber.
So 800 members is an improvement. Rather than size of the membership, the problem is its appointment and composition. memberships are given to political friends and the candidates often very weak. So a properly elected chamber by the people, not by politicians has to come. I am not bothered if membership is 800 or 8000 as long as it is representative and chosen by the people. It can be argued that there should be more Lords because their job is to scrutinise the crap that comes from the Commons.
The elephant in the room is the number of MPs, which should be halved. With improvements to communications and more information readily available to anyone, the number of local representatives needed to fulfil the local democracy aspect, is less than it was.
http://researchbriefings.files.parliament.uk/documents/LLN-2016-0006/assets/4a603d73-ce97-4fb8-ac65-367b2bc8112f.png