The National Gallery in London is facing the prospect of major strike disruption during next month's Leonardo da Vinci blockbuster exhibition, the Observer has learned.

Warder staff are considering industrial action in protest over security cuts that they warn will make works of art more vulnerable to damage or theft. The action would take the form of walkouts for an hour or two at a time, necessitating the evacuation of the building.

News of the protest comes after a man vandalised two Poussin masterpieces last July with paint.

Under pressure from government cuts, the gallery has instructed its warders – now called "gallery assistants" – to each watch over two rooms rather than one, as previously. Warders claim the new arrangement allowed the Poussin vandal time to attack two paintings because the warder was in the adjoining room.

About 200 members of staff – including curators – have signed a protest petition to the gallery's director, Nicholas Penny.

The gallery is expecting record numbers of art lovers for an exhibition of the "largest ever number of Leonardo's rare surviving paintings", including international loans. It is due to open on 9 November, when an initial protest could begin.

Negotiations between the gallery and its assistants are being conducted by the Public and Commercial Services Union (PCS). An indicative ballot is being run to test the mood for strike action. "They're keen to do something now," a PCS spokesman said.