We had come to a cathedral of British learning, hoping that the same institution that nurtured Karl Marx and Charles Dickens would equally inspire us to feats of erudition and scholarship.

We face problems, however — issues that Marx never had to grapple with as he sat and thought in the Reading Room of the British Library, which opened in the British Museum in 1857.

There is the surprising robustness of the capitalist system, the triumph of relativism, and most pressing of all, a general shortage of places to sit.

“I’m afraid we are rather crowded at the moment,” said a lady at the registration desk where I had pitched up to register for a reader’s pass.

“The place is full of panicky students with a few weeks left to finish their dissertations.”

No bags are allowed into the reading rooms and in the bag storage room downstairs, a dignified scramble was under way for the last remaining lockers.

Mary Wu, a retired teacher taking a BA in fine art, stood and waited for another reader to evacuate his possessions, like a motorist waiting for a parking space.

It is two years since the library opened its doors to undergraduates. Young students now flock to its quiet spaces and pile up on benches and balconies in the high-vaulted front hall, sparking a backlash from the library’s more established residents.

In The Times yesterday Lady Antonia Fraser told of long queues. The historian Claire Tomalin felt the policy was “access gone mad”.

On one particularly frantic day last week, the author Christopher Hawtree was exiled temporarily to a windowsill.

Being an economist, Marx would have been familiar with the concept of scarcity. But would he have been able to finish Das Kapital in a place that, according to the historian Tristram Hunt, has become “a groovy place to get a frappuccino”?

Perched on a bench on the first floor balcony, Jenny Chamarette, 26, was working on her PhD in French cinema and contemporary French thought.

“This is a really lovely space for serious research,” she said. “The arrival of undergraduates has had an impact on how the library feels. It’s particularly bad during the vacation.”

She added: “If you are an undergraduate, the need for the depth of the material that they have here is less acute. The need for the serious researcher is more acute.”

Marx might perhaps have suggested a redistribution of assets, “from each according to his abilities, to each according to his needs”.

Such a radical reallocation of desks appeared less urgent yesterday afternoon, however. The Humanities Reading Room was certainly crowded but there were gaps in the ranks of quiet readers. During the height of the Easter holidays, the room was occasionally declared full and closed to arriving scholars.

Louise Raw, 41, who is 100,000 words into a thesis on the women’s strike at the Bryant & May match company in 1888, was turned away recently, having travelled from Hertfordshire.

“I was told they were completely, fully booked,” she said. Still, she does not believe in banning undergraduates. “It is such a wonderful place to study, I don’t believe people should be excluded.”

In the library café, three young law undergraduates from the London School of Economics said that they couldn’t use their university library because it was always fully booked.

Sarah Davies, 22, a student at Goldsmith’s College, admitted that the library had become crowded, “but recently I have been using the Rare Books Reading Room,” she said. “That is quieter.”

Theresa Dean, 53, who is researching a book on the Israeli-Palestinian conflict, said: “You should tell Lady Antonia Fraser that she’d better come early, before the students are up. It does get busy here but you just have to work around it.”

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