David Bellamy, the conservationist and a member of the zoo's council, resigned immediately after the vote, at a meeting of 250 of the 2,000 fellows of the Zoological Society of London, the zoo's parent body. The rest of the management are considering their position.
The mood of the meeting was said to be united. Its theme was that the zoo could be made to be viable, but that the current management team had so little credibility that neither the Government nor investors in the City were interested in talking to it about rescue plans.
The vote puts moral pressure on council members, management and executives of the zoo to stand down en masse at the society's next annual general meeting on 30 September. They may call a postal ballot to check the views of fellows not at the meeting.
As he left what one fellow described as 'a very angry and bad-tempered' meeting, Mr Bellamy said: 'We are now on the route to being able to say London Zoo is not going to close.'
He said he would consider standing for re-election if asked, but added: 'It's a cowardly way out but somebody had to make that move. I have taken that lead and I hope others will follow.'
The first resolution yesterday - that all those in management responsible for June's decision to close should step down - was passed with 184 in favour, 32 against and 9 abstentions.
The second - that all possible steps be taken to keep the zoo open as a National Centre for Animal Conservation - was passed with 157 votes in favour, none against and 7 abstentions.
Yesterday's special general meeting, convened after more than 70 fellows signed a petition, was a victory for the Reform Group of dissident fellows.
Dr Simon Bearder, a founder member of the group and a lecturer in anthropology at Oxford Polytechnic, said his group did not object to individuals on the management, but had to call for 'the good, the bad and the ugly' to resign so that the good could be re-elected democratically.
Professor Tim Halliday, who is due to take a zoo council post in September, said as he left the meeting: 'I don't see how they can oppose the membership now with a vote of that strength.'
Sir John Chapple, president of the society, said the management could not walk out after the vote because as trustees they were legally responsible for overseeing the society's affairs as a charity.
Dr Stephen Cobb, another member of the Reform Group, said: 'There is no question that the zoo will stay open one way or another.' He said his group had re-calculated the financial resources available to the zoo, showing that it did not need to close.
The elections expected at the end of September would be 'the first time their (the management's) record and capabilities will have been put to the fellowship.'
He also raised the threat of court action against the management if after yesterday's vote they refused to resign and decided to go ahead with closure. 'The fellows think they have improperly fulfilled their responsibilities as trustees.'
Sir John said it would be wrong to say that he was in a position to overturn the decision to close. But he thought that 'the tone and tenor of the meeting was that the zoo will be saved'.
He added: 'I have to look after the interests of the people who work here. They would dearly love me to say on my authority that we can stay open, but I can't do that.'
Between now and September, the current managers will continue discussions with New Zoo Developments, the consortium led by David Laing of the construction family, that is offering to raise pounds 61m of investment to transform the zoo into a modernised attraction.
The zoo is not bankrupt. Last June, Sir John said it had sufficient reserves to cover the costs of an orderly closure at the end of September. The recent gift of pounds 1m from the Emir of Kuwait has also helped bolster its resources.
In the past six weeks, attendances at the zoo have been sufficient for it to meet its budget day-to-day.Reuse content