Cuts imposed by ministers that will see 125 jobs axed at Kew Gardens have gone ahead despite warnings that any drop in resourcing would threaten its future as one of the world's leading botanic institutions.

A reduction of £1.5m in funding from the Department for Environment and Rural Affairs (Defra) coupled with other financial pressures have contributed to a £5m hole in Kew's budget that managers say cannot be filled without losing a sixth of the institution's staff, mostly in scientific areas.

So serious is the situation that one leading scientist is warning that Kew is in the "last chance saloon" – while one former trustee, BBC journalist Anna Ford, called on the organisation's wealthy patron Prince Charles to bail it out.

According to internal documents, Kew managers have drawn up a budget that will see 90 jobs go this calendar year, with the rest soon after. Compulsory redundancies have not been ruled out.

But the cuts were approved against the advice of consultants for Defra, who told ministers in 2010 that Kew would lose its world class status and see its research decline below a critical level if its operating grant was not maintained from 2012 onwards.

An Italian Maple tree coming into flower at Kew Gardens in 2009. Photograph: David Levene for the Guardian

A report Defra commissioned from Sir Neil Chalmers, former director of the Natural History Museum, found that Kew's scientific work was already suffering from a lack of funds that meant key vacancies had not been filled.

The report, published in 2010, said the problem was exacerbated by staff being diverted from core research to money-making activities. It called on Defra to ensure Kew received an operating grant that at least maintained its value in real terms from 2012 onwards. Without proper funding "Kew's future will be threatened," the report said.

Professor Hugh Dickinson, a plant scientist at Oxford University who worked on the Chalmers report, said: "Kew is not only in the last chance saloon, the bell is ringing. The UK was a world leader in the area of plant science from Victorian times onwards, and it's going to become increasingly important. Kew is a key component of the machine that will do this work. We'll be kicking ourselves if we let it slide."

The Royal Botanic Gardens in west London has been a world class centre for botanic research for more than 250 years. The Unesco world heritage site draws two million visitors a year to its historic buildings and spectacular plant collection, which ranks as the largest in the world.

Anna Ford. Photograph: Rex Features

Kew's collections and its scientists are globally recognised as an invaluable resource for research on biodiversity, climate change, conservation and crop improvement. Their grounds at Wakehurst Place, West Sussex, house the Millennium Seed Bank, an international conservation project that aims to preserve plants worldwide.

Ford, a former BBC journalist and trustee of Kew in the 1990s, said: "For Britain to have a world heritage site that's treated with such miserable parsimony is quite shocking. I feel a sense of despair.

"How can you keep the place going at that level of staffing? It's a form of bullying. Defra is saying to Kew you're just another way we can save money and slash things and don't you dare complain.

"Prince Charles is the patron. He is worth millions. He could give them bags of money, but I doubt that he will."

The waterlily house at Kew Gardens in May 2013. Photograph: Jacob Carter/Rex Features

Information about Kew's financial crisis has been circulating for some months but presentations by Kew managers, seen by the Guardian, reveal where the jobs will be lost. It is proposed that the largest proportion of jobs, between 40 and 50, will go from Kew's science directorate, a further 35 to 45 from public programmes, and 25 to 30 from corporate services. The remainder will go from horticulture, Kew's Innovation Unit, and Wakehurst Place.

To help plug the gap, Kew is looking for sponsorship deals that could include naming rights for its historic buildings – and expects to increase the admission price of £14.50. It has already introduced car parking charges on its West Sussex site.

Richard Deverell, director of Kew, said Defra had fought hard to minimise the cuts, and played down the impact they would have. "Many public institutions are facing reductions in their funding, and Kew is not exempt from that," he said.

Zac Goldsmith. Photograph: Steve Parsons/PA

"We've had some hysterical responses from people that this is the end of Kew science and of course it isn't at all. Kew employs 300 scientists. Inevitably there will be fewer, but not that many fewer. I am absolutely confident that Kew science will thrive."

But already more than 73,000 people have signed a petition calling on Owen Paterson, the environment secretary, to reverse the cuts. David Attenborough, the WWF, the Society for Biology, several major unions and a global network of scientists, educationalists and horticulturalists have all made public statements expressing their concern. John McDonnell, MP for Hayes and Harlington, has tabled an Early Day Motion calling for a public debate on the implications of the cuts before any final decisions are made.

Zac Goldsmith, whose constituency of Richmond Park and North Kingston is home to Kew Gardens, said he had written to Defra ministers to raise concerns over the cuts. "It's not clear to me that Kew Gardens can sustain its extraordinary work with the level of cuts being imposed.".

A fall in the operating grant from Defra accounts for £1.5m of Kew's financial woes. A further £2m of the deficit is due to reduced funding from the Kew Foundation, which has bailed out Kew Gardens in the past two years, but can no longer sustain the payments. Automatic pay rises and higher utility bills deepened the hole by a further £1.5m. Kew's gas and electricity bill alone was £1.4m last year. But the rest of the budget hole will be filled by making posts redundant.

The job losses will reduce the breadth of the institution's research, though areas where Kew is particularly strong, or can make an income, will be saved. "There will be a bias towards protecting those areas of science that have the greatest potential to generation income," Deverell said. "The organisation is trying to do too much and its resources are spread too thinly, and inevitably I'd much rather we did fewer things and we did them to a genuinely world-class standard and made a really important contribution in those fewer areas." The details will be finalised in the summer.

A Defra spokesperson said on Thursday: "Since 2010/11, Royal Botanic Gardens Kew has received £114.5m in government funding – like all departments we are making savings and playing our part in reducing the deficit, but we are pleased we have been able to offer relative protection to their funding. The Chalmers report dates back to the previous administration and reflected Kew's financial status at that time."