Supporters of the Oxford don who was sacked from her post as Royal Institution director will tomorrow try to dismiss its entire leadership

Several hundred of Britain's most distinguished scientists will gather tomorrow in a modest, steeply banked lecture theatre in London's Mayfair to determine the fate of the world's oldest independent research body, the Royal Institution.

They will debate a motion – described as "unprecedented in legal history" – that would dismiss its current council and replace it with supporters of the institution's former director, Lady Greenfield.

Susan Greenfield was sacked on 8 January following massive cost overruns incurred during a major refurbishment of the institution's headquarters that she had instigated. But now her supporters are mounting a dramatic bid that could lead to her reinstatement.

They say Greenfield is a victim of sexism and want to impose a completely new "transitional council", made up of their own members, on the institution, which is based in Albemarle Street, Mayfair. They claim the move would save the organisation – whose directors have included Michael Faraday and Humphry Davy – from ruin.

One supporter, Professor Lisa Jardine, of St Mary's College, London, said Greenfield was likely to win "anything between £500,000 and £1m" at an industrial tribunal because of her treatment. "That would only exacerbate the institution's financial crisis. However, the present council has boxed itself in over this," she added. "They are funny boxed-in clique and we are trying to free the institution from their influence."

However, opponents say the plan would sabotage efforts to refinance the debt-ridden institution. "A move like that would see the closure of the institution within six months," one member told the Observer. "This is a fight for the life of the Royal Institution."

Greenfield was appointed director in 1998. It was hoped that a charismatic, media-friendly new leader would sweep through the institution and introduce new ways to raise funds and popularise science in a body that was widely recognised as being badly out of date.

The appointment was controversial but necessary, said Jardine. "You either love or hate Susan. No one ever says 'she is quite nice'. However, she is a bloody distinguished neuroscientist."

But Greenfield's attempts to generate funds were unsuccessful and the institution was forced to sell its portfolio of properties in a bid to pay off debts incurred in refurbishing its building. It is now £2.5m in debt, with an annual operating loss of around £1.75m. "Only a major charity can save us, and so far we haven't found one who seems interested in our survival," said one member.

Nor are its problems helped by the furore over tomorrow's vote. "Corporate organisations work on the principle that you have a rotation of members on its council or trustees," said Frank James, professor of history at the institution. "But this motion seeks to replace totally the existing council. The idea is unprecedented in legal history."

It is also a concept that alarms many scientists. "If you replace the whole council, that will bring a great deal of instability," said Dame Nancy Rothwell, the Manchester neuroscientist who presented the institution's 1998 Christmas lectures. "It would disrupt all the RI's efforts to raise cash, which is why the staff have urged against the plan. "

Many, including Rothwell, warn that if tomorrow's vote is in favour of the transitional council the Royal Institution would close within months. The 211-year-old organisation was set up primarily to promote scientific understanding among the public and for much of its history it succeeded spectacularly, with its lectures being regularly sold out in the 19th century, while in the 20th century its Christmas lectures, televised by the BBC, were watched by millions.

But science popularisation has become a highly sophisticated business. Young scientists such as Brian Cox and TV series like The Wonders of the Solar System bring glittering scientific images into homes, while the Science Museum and the Wellcome Trust have proved adept at scientific showmanship, presenting complex issues – including shows on stem cell research, DNA databases and other subjects – in a highly accessible manner. By comparison, the RI has lagged badly behind. "Susan deserves great credit for all she did to pull the RI into the modern era," said Oxford neuroscientist Professor Colin Blakemore. "But it now needs someone else to find a niche for it this century."

For her part, Greenfield insists she is a victim of sexual discrimination. "I was unfairly dismissed," she told the BBC on Friday. "I am female, and it is my contention that a man would not have been treated in the same way."

Greenfield has warned that she will take the matter to an employment tribunal at the same time as her supporters are plotting to replace the council.

It does not bode well for the future, said Blakemore. "Whatever the merits of the various claims, this dispute and the attempt to install an inexperienced council and to reinstate Susan are only going to do further harm to the Royal Institution's chances of survival."