A high-minded attempt by the National Gallery to replace populist blockbuster shows with exhibitions of lesser-known artists has led to a collapse in paying visitor numbers, internal figures have shown.

The gallery in Trafalgar Square has hosted two exhibitions this year, both of obscure Italian painters. The more successful is on course to bring in 30,000 visitors – a 10th as many as went to see Velazquez in 2006. The other sold just 19,000 tickets.

The gallery’s performance is slipping behind those of comparable venues such as the British Museum, whose Chinese exhibition The First Emperor attracted 850,000 people. The Royal Academy and Tate Modern have also mounted popular shows in recent months.

The figures present a problem for Nicholas Penny, the gallery’s recently appointed director, who – although he did not commission the flops – came into office arguing that the gallery hosted “too many blockbusters”.

Penny’s arrival came amid turmoil in the gallery’s senior management. His predecessor, Charles Saumarez Smith, oversaw successes including the Velazquez show, Vermeer in 2001 and Titian in 2003, which each drew about 300,000 visitors. He left after falling out with Peter Scott, the former chairman.

The decline in visitors will be one of the main challenges confronting Mark Getty, the new chairman, whose first trustees’ meeting takes place this week. He is the son of Sir Paul Getty, the American-born oil tycoon and philanthropist.

The gallery is facing a further test of its finances – it has only four months to raise half the £50m needed to keep Titian’s Diana and Actaeon, currently on display at the National Gallery of Scotland, from being sold on the open market by its owner, the Duke of Sutherland. The two galleries are working together to try to save some of the duke’s paintings.

Although entry to the National Gallery’s main collection is free, the institution relies, like other big museums, on paid exhibitions for part of its revenue. The National will receive £25.5m this year from the government; it earned £13m last year from commercial revenue, including exhibitions, and from donations.

The poor attendance – with last year’s figure of 4.1m visitors also falling – could damage the gallery’s ability to obtain government funds. The culture department’s policy is to “reward successes” and give extra money to galleries that attract large numbers.

Exhibitions last year drew about 70,000 each, but this year numbers have fallen sharply. A show of work by the 18th century Italian Pompeo Batoni, which ran from March to June, drew fewer than 19,000 paying visitors, just 45% of its budgeted figure of 35,000. Radical Light, which ends next weekend, is on course to attract 30,000, also in three months. The exhibition, featuring Italian art from the turn of the 20th century, was meant to bring in 50,000.

At his first press briefing in February, Penny said: “There are too many blockbuster exhibitions today, which show people what they already know.” In an interview last week he would say only: “We so much need to sort out our exhibition programme.”

There may be some recovery later this year, with names such as Holbein, Raphael and Titian included in the exhibition Renaissance Faces. It is not expected, however, to draw more than 100,000 visitors, particularly because it faces tough competition from Tate Britain’s Francis Bacon retrospective, opening next week.

Big crowds are not expected again at the National until April next year, when it shows an exhibition about Picasso and his influences, such as Degas and El Greco.

Additional reporting: Solvej Krause

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