The move comes as the museum – the world’s leading authority on conflict – plays its part in marking the centenary of the outbreak of the First World War.

When prime minister David Cameron reopened the museum in July 2014 he said: “When I launched our plans for the First World War centenary, I said that the renovated Imperial War Museum would be the centrepiece of our commemorations. And what a fitting centrepiece this is – a national focal point in which we can all take great pride.

“You have created something fitting and lasting – something of which we can all be proud.”

Prospect negotiator Andy Bye said: “Closing IWM’s library is not a fitting way to mark the centenary of the outbreak of the First World War. IWM aspires to be a highly respected authority on its subject matter, but this will be impossible without a library.”

IWM London’s library acquired its first item in 1917 and has been a vital part of the museum ever since, playing a key role in helping staff do their jobs whether curating exhibitions or helping them to understand and identify artefacts. It also provides members of the public with access to research materials.

The closure has also been proposed of the ever-popular Explore History facility in London. Open seven days a week it allows the public to explore IWM’s collections and find out about objects and subjects not on display. It attracted 55,000 visitors last year.

School educational visits, led by museum and education professionals, to IWM branches at Duxford, HMS Belfast and the Churchill War Rooms are yet another service under threat.

The possibility of closures and cuts comes at a time when demand for all the museum’s services has never been higher: the IWM attracted 433,000 learners in 2013-14 and 256,000 children took part in its on and off-site educational programmes.

“Prospect fears this is only the start and that further damaging cuts are likely,” added Bye.

The petition is at http://bit.ly/save_IWM.

The prime minister’s speech is at www.gov.uk/government/speeches/reopening-of-the-imperial-war-museum-david-camerons-speech.