I'm not really sure the point is even worth making...
Free attractions in London (notably the museums, the closest example being the NHM with their spirit collection and live insects for research) are either partly or majority funded by the state, often with large income from the National Lottery. British Citizens pay for this, but at a cost that is negligible. Still, tourists get the benefit of entering for free without contributing to the upkeep unless they spend inside. I have no problem with this, and it's an excellent way to ensure education and historic buildings like that are open to all.
ZSL does not get government funding, local or national. This is different to most zoos on the continent, especially Germany, that have either direct funding or energy subsidies applied often. ZSL is, unfortunately, on its own. But equally London and Whipsnade are both just one part of ZSL, and a large proportion of ticket price goes towards the more important parts of the charity - research, in-situ support and education. The zoos are technically a branch of the education section, oddly enough. If you go to the zoo, you pay the cost of all of this, whether you are a British national or not. This is the unfortunate reality of not being subsidised. But more importantly - you cannot compare either ZSL collection with any of the other free attractions in London. Many of us on this site have worked with or at zoos, and I'd wager quite a few of us also have experience in non-zoological attractions as well - the daily costs, let alone upkeep, developments, staffing and events - of a zoological collection are astronomical compared to something like a museum.
If ZSL could double ticket sales, I doubt they'd even reduce ticket cost that much simply because the investment required for that increase in sales would have to be astronomical. For one, moving the entrance of the zoo closer the tube lines (something floated about previously but abandoned due to cost). Someone replied to me before this thread was moved stating London Zoo is easy to get to. Compared to Whipsnade, perhaps. Compared to Berlin, Prague, Leipzig? God no. You have a half hour walk (40 minutes now one of the main routes is closed) from either Baker Street or Regent's Park station, or you can get a bus that takes an annoyingly long time stop-starting around Regent's Park after getting the tube to an appropriate station. To go to the NHM you step off the underground and walk 5 minutes through a tunnel. It is an unfortunate reality that tourists, when offered with the choice of an expensive zoo that's moderately annoying to get to or a museum that also has animals in it, is free, is easy to get to, and has 2 more museums next door, will choose the easy option 9 times out of 10.
I'm aware I've gotten off-topic from the original point about paid entry vs free but it was things I wished to say in the previous thread but didn't want to derail it. All of this applies to BZS and BZP and they don't have the advantage of having a fully-stocked open zoo to help with funding currently. The BZP entrance fee is steep for the species list but for the experience it certainly isn't, especially considering the conservation work that hasn't stopped in the background.
The London Zoo ticket is, for what it's worth to me, a price that's steep but deserved. If I could take £5 of funding per person that subsidies the NHM's entrance fee and give it to ZSL I would in a heartbeat, if just to give the NHM a kick up the arse to actually add a new development as opposed to occasionally dusting 30-year-old halls, but alas that is not the world we live in.
ZSL and, apparently, BZS are both in fairly good financial situations currently. ZSL more so, I'd imagine. If they had public funding or even massive private funding like zoos on the continent they would be world beaters in every sense of the word. But they don't, so I think we should commend the job that they have done especially in recent years wrangling costs and developments.
Even for me this hasn't been a particularly coherent reply but I hope the point has got across. I'm honestly not entirely sure what the point of the original thread was beyond moaning about ZSL and BZS again for the sake of it. But anyway, that's my opinion on the matter.