Around a third of staff at Bletchley Park are set to be made redundant due to the impact of the pandemic.
The site in Milton Keynes is famous for being the home of the World War Two codebreakers whose work saved thousands of lives.
The Bletchley Park Trust, which runs a museum at the site, lost 95% of its income during lockdown and expects to lose £2 million by the end of the year.
In a bid to urgently save money and reduce the size of the team, bosses have proposed a restructure which would result in 35 people losing their jobs.
Workers were told the news on Friday and a consultation period will now begin.
Chief Executive Iain Standen said that the trust had "exhausted all other avenues".
"The economic impact of the current crisis is having a profound effect on the trust’s ability to survive," Mr Standen told staff.
"We have exhausted all other avenues, and we need to act now to ensure that the trust survives and is sustainable in the future.”
The trust has already tried to make savings by reducing marketing, new exhibitions, travel, IT and printing costs, but these steps will only help in the short-term.
Like many businesses, the trust closed its doors in March and re-opened again in early July, although social distancing rules have meant they have only been allowed to welcome a fraction of the visitors they would normally expect.
The trust furloughed 85% of its staff at the start of lockdown and managed to secure some additional funding from the National Lottery Heritage Fund, but Mr Standen admitted that jobs cuts would now be a necessity to ensure the trust's future.
“I cannot stress how deeply saddened I am to announce the need for such a severe restructuring," he said.
"We have built a brilliant team on the back of huge success and with great ambitions for the future, which we will now need to re-examine. I had hoped that we might avoid the need to do this, but we find ourselves with no other choice if we are to secure the future of the Bletchley Park Trust.”