Deborah Swallow might not have as high a profile as some of her predecessors, but as one of the former directors of the Courtauld Institute of Art was the Soviet spy Anthony Blunt this is hardly surprising.

Blunt's presence is still felt at the Courtauld, having spent nearly 30 years there before leaving in 1974, five years before his espionage was made public by the then prime minister Margaret Thatcher.

Swallow has had less time to make her mark on the organisation, which is based at Somerset House in London. She joined in 2004 after James Cuno left for the Art Institute of Chicago following only 18 months as director. Christopher Green, the acting director during this period, said at the time: "There was the steepest fall in morale that I can remember."

When Swallow arrived, she not only had to tackle the fallout from Cuno's sudden departure, she also had to deal with an institution that had become self-governing only two years before, having decided to become an independent college of the University of London. That she was there at all was a surprise to Swallow, who had not seen herself as a candidate when the job first came up.

"I never dreamt of applying, as I assumed I wasn't qualified," she says. "The Courtauld has primarily been a centre for the study of western art and art history, and I never had formal training as an art historian and am an Indianist. But I was encouraged to apply and then it became more and more interesting. I was flabbergasted when I got the appointment."

Swallow started the job in 2004 with the remit to expand the Courtauld's sources of funding, build on its new status as a self-governing body, and to make it better known to the wider world.

The chance to raise the Courtauld's profile soon arose, as its 75th anniversary covers the 2007-08 academic year. "One of the agendas is to remind people that we exist, but more than that, it is to clarify what we are," says Swallow. "One of the problems that we have all been aware of is that people either know the gallery or the institute."

The gallery, with its permanent collection and temporary exhibitions, is very much the public face of the Courtauld. As an academic centre for teaching art history and conservation, the institute is better known by those working in museums and galleries. For Swallow, the trick is to get the various elements that make up the Courtauld to operate in harmony.

"The key is that all the assets of the Courtauld should work together as creatively and as well as they possibly can," she says. "Academic art history, the teaching and research, its fantastic collection of art, the conservation departments; each strengthens the other and gives dynamism."

Raising the profile of the Courtauld is aided by its excellent art collection, which means it can hold temporary exhibitions on Renoir, Cézanne and Turner during its 75th anniversary. Having an important collection also means it can charge for entry to the gallery.

"It does not bring in huge amounts, but is significant enough that we would find it hard to replace that money," says Swallow. "We have very high visitor numbers on Monday morning when we are free to the public. Many people would love it if we could afford not to charge."

The Courtauld is also kept in the public eye by a high-flying alumni that reads like a who's who of the museum world: Tate boss Nicholas Serota, British Museum director Neil MacGregor, and Mark Jones, the head of the Victoria and Albert Museum, all studied there.

These high-profile associations are a far cry from Swallow's first museum job - as an assistant keeper at the University Museum of Archaeology and Anthropology in Cambridge. Again, it was a job that she did not actively seek.

"Did I plan to get involved in museums? Absolutely not - it happened to me. I was doing my PhD at Cambridge and did not have a job. One came up at the University Museum of Archaeology and Anthropology and my supervisor suggested I put in for it, and I got it. I was like a duck to water - I loved it.

"The museum had a huge housekeeping problem and I had the fun of working through the ethnographic collections," adds Swallow. "You opened cupboards behind display cases and everything literally fell out. It was wonderful. And it was phenomenal informal on-the-job training, where you were thrown in at the deep end at every level of museum work."

Before starting work at the museum, Swallow spent a couple of years teaching English in India as a volunteer with VSO. She has retained a lifelong interest in the country - she still visits often - which led to a move to the Victoria and Albert Museum (V&A) in 1983.

Her knowledge of India and the wider region could also pay dividends for the Courtauld, which is looking at ways for its teaching of art history to stay relevant. One possible route is expanding its focus beyond western art.

"I am quite keen on finding interesting ways of working more with the Middle East and Asia," says Swallow. "It is very much my own personal passion, but because of that, I am also as sensitive as you can be about the complexities and the need to do it well."

One change Swallow has overseen is the introduction of a new MA course in curating art museums. She is also looking at other areas with a direct professional connection, including something in heritage.

A major challenge for Swallow is for the Courtauld to be a success in the wider context of Somerset House, where it occupies the buildings on the north side. Somerset House was recently hit by the double blow of the transfer of the Gilbert Collection to the V&A and the closure of the Hermitage Rooms (Museums Journal November 2007, p5).

The Courtauld was not responsible for the Gilbert Collection, and the space it occupied will open in April as a temporary exhibition space called the Embankment Galleries.

But the Courtauld did manage the Hermitage Rooms. "We have an academic alliance with the Hermitage, and that relationship is continuing," says Swallow. "But there was no way we could carry on underpinning a very significant ongoing funding. Now it will be more project by project, which is sometimes easier."

The anniversary year has been a good opportunity for Swallow to look ahead to future challenges, but also to think about the contributions of past Courtauld directors, particularly Blunt, who was not supported by the institution after his exposure as a spy.

Swallow recently appeared in a BBC Newsnight item about Blunt that discussed how the spying revelations destroyed him and meant his contribution to art history in the UK has been largely forgotten.

"The time has come to revisit his contribution as the head of this institution and as a wonderful art historian," says Swallow. "It was he who shaped art history in this country and the faculties throughout the country. He was a fantastic networker and obviously a magnetic teacher."

Swallow is clearly very different from Blunt. It seems unlikely that she is hiding a double life as a secret agent, even if they did both study at Cambridge. But she does hope she can also make a mark on an institution that has played a major part in the history of UK museums and galleries.

Renoir at the Theatre, the second of three exhibitions celebrating the Courtauld Gallery's 75th anniversary, runs until 25 May