Gallery assistants are going on strike and it's crucial we pay attention

Anyone who spends as much time as I do in museums and galleries must speculate about the lives of those quiet, almost invisible people who guard the treasures. Every now and then I've got into conversations with gallery and museum assistants, and found them unfailingly interesting and intelligent.

I recall a long dialogue with an assistant at Kenwood House in north London about the two circles in the background of the great, late Rembrandt self-portrait that is the pride of the collection. He had some quite involved and abstruse theory about what the circles represented (they continue to puzzle art historians). Although I can no longer recall the details of the theory, I will not forget the intensity with which he expounded it. I found it touching that, rather than being content with the role of jobsworth, he had thought long and hard about the masterworks in his care.

There is a ruminative film called Museum Hours by Jem Cohen which concerns an unlikely relationship – even a kind of romance – between a museum assistant and a visitor to the Kunsthistorisches Museum in Vienna. As the title suggests, the film is as much about time and time's passing as it is about the museum and its wonderful works (in this case particularly the Bruegels). The wry, sensitive assistant played by Bobby Sommer is a man in his sixties, thoughtful, wise and compassionate, as interested in the people he observes as in the artworks he guards: "I used to work in the music business," he says near the beginning. "I had my share of loud; now I have my share of quiet."

Museum assistants may be among the few people in the frenetic contemporary world who have "time to stand and stare" (or more likely sit and stare) as the poet WH Davies put it. They are also people invested with awesome responsibility – to protect works that are vital, living organs of our culture but that are also terrifyingly fragile and vulnerable.

Getting such modest, undemonstrative people to go out on strike is quite an achievement. The assistants at the National Gallery in London have now been on strike intermittently for several months in an ongoing dispute about the proposals to privatise visitor services. Stories have appeared in the press suggesting first that this is an unprecedented move and secondly that these devoted custodians of masterworks, if re-employed by a company such as Serco or G4S, might find themselves guarding supermarket car parks.

Showing me round the gallery at nine on a Monday morning, the outgoing director Nicholas Penny scotched both those suggestions as "myths". He seemed as saddened as I am by the ongoing and disruptive industrial action (on strike days some galleries are closed), touchingly concerned about the works in his care, and infectiously enthusiastic about small details such as a strange fish in a Perugino altarpiece.

He praised the devotion beyond the call of duty of the staff – "the record of assistants leaping to the defence of paintings is between good and heroic" – and, all things being equal, voiced a preference to keep visitor services in house. But his modernising plans – more events for members and corporate supporters, more flexibility of working hours – appear to have come up against unyielding resistance from staff and their union.

My impression was of a man with the best of intentions for an institution he has served devotedly and wishes to leave well prepared for the future. At the moment, though, the Gallery is passing through a perilous time. The worst thing that could happen is an attack on one or more of the masterpieces (remember that in 1914 Velázquez's Rokeby Venus was slashed several times with a meat cleaver by the suffragette Mary Richardson). The second worst is that a visitor experience which has always been positive might be soured, that a particular culture of looking after paintings might be destroyed.

Just now, I fear, both these possibilities seem more likely. It is the worst of all possible worlds. Perhaps it is an unavoidable part of what the American critic Francis Fergusson, speaking of Chekhov's The Cherry Orchard, called "the suffering of change".