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Just like every other school in Britain, Eton College is under pressure to squeeze as much teaching space as possible out of its premises. It may boast a bank balance that public-sector schools would die for, but the toff's private school does face one overriding constraint to development – the strict listed building and conservation area designations of its medieval campus.

Local architect Corrigan + Soundy + Kilaiditi has just completed a particularly radical refurbishment of the historic New Schools building at the heart of the college's campus. Built at a cost of £3.3m, the refurbishment has reconfigured internal circulation to make room for teaching and staff accommodation and added two extensions. A total of 800 m² of additional floor space has been added, increasing the building's area by 25%. In designing the alterations, the architect has not been overawed by five-and-a-half centuries of built heritage. Although mostly hidden within the existing building envelope, the new interventions have been boldly expressed in contemporary materials and style.

The New Schools building was originally created as a fitting neighbour to the college's fan-vaulted chapel of 1440. Its Tudor arcades, battlements, diaper brickwork and elaborately carved stonework, however, are all a sham – albeit a meticulous sham – as the H-shaped block was completed in the mid-19th century by the Victorian architect Woodyer. The grade II-listed building is now occupied by the thoroughly modern and burgeoning faculties of maths, geography and information technology.

In the elongated wing of the mathematics faculty, original staircases at either end have been stripped out and replaced by a single staircase inserted at the heart of the block. The removal of the original staircases has released space at either end for staff rooms. The new staircase was created by cutting a large slot from the roof down. Daylight is funnelled through the slot into the heart of the building, and encounters minimal obstruction from the clear-glazed balustrading and open steel stair treads.

In the same wing, the original pitched roof has been replaced with a top storey of classrooms. This is contained within a shallow-curved zinc roof and window walls set back from the old brick battlements. Although overtly modern and clearly visible from the courtyard below, the transparent window walls and clean-cut eaves line make the new top floor appear to float above the heavy masonry structure below. As a bonus, the appendage actually weighs less than the slated double-pitched roof it replaced and so required no structural reinforcement to the existing walls.

In the central block, occupied by the geography and IT departments, a similar exercise in space making was carried out. Here, rickety wooden staircases within two corner towers were removed to provide teaching space. They were replaced with slender spiral staircases that cantilever into the central hallway.

The boldest new intervention is the replacement of an undistinguished single-storey extension to the central block, which had been erected in the 1930s. Here, Corrigan + Soundy + Kilaiditi has opted neither to match the mock-Tudor brickwork of the original building nor to create a modern lightweight structure like the roof extension. Instead, the architect has gone for a massive structure with battered – or tapering – curving walls in Portland stone and deep-set windows. Associate Dido Milne explains: "We were mindful that the 1930s extension looked as if it had been tacked on the strongly symmetrical building. We have used the same materials in a different way, as we wanted something abstract and enigmatic. One wall is curved to lead naturally round to the main entrance to the department."

Milne admits that the bold new curved extension has its detractors as well as its admirers in the college. On a more positive note, she adds: "The maths department likes the way the reconfiguration integrates the department for the first time and gets more daylight into the building." With practical benefits like these, the latest addition to the Eton campus should take much less than five-and-a-half centuries to gain acceptance.