Curved and angular bay windows animate the stepped facade of House on a Hill, a penthouse in central London designed by local studio David Kohn Architects.

The three-storey home sits atop a Victorian warehouse building in Smarts Place, Covent Garden, and is described by David Kohn Architects as a "house on a hill".

Rather than treating the project as an extension of the brick block below, the studio imagined the roof as a new ground plane, using familiar elements of residential architecture such as bay windows.

"The two-storey tiered extension responds to the richness of the surrounding rooflines, and its plan recalls those of pre-modern town houses with an arrangement of living rooms with projecting bay windows," said the studio.

"The project recalls many precedents from domestic architecture through the ages – Sir John Soane's Museum to the Villa Necchi in Milan – and previous practice projects, from Red House to A Room for London," added founder David Kohn.

"The design nonetheless strives for a specific response to site and an attitude to life today," he added.

The distinctive bay windows of House on a Hill define a strip of living spaces along its southern side, with a dining room, library and lounge that can act as either individual rooms or a long enfilade opening onto a rooftop terrace.

Offering sun-shading and privacy to both these terraces and the south-facing bay windows is an arrangement of trees and plants designed by landscape architect Todd Longstaffe-Gowan.

"The three main living spaces – living room, library and dining room – each have a different geometry and relationship to skyline views but no doors between them," Kohn told Dezeen.

"So they can either be enjoyed independently or as an enfilade for a party," he continued. "From each interior, you look through a densely planted and treed garden at a skyline view of central London. It is a retreat from the centre, at the centre."

The library is wrapped by a high, curved shelf that follows the geometry of the bay window, while overhead in the living and dining areas are ceilings of subtly undulating plasterboard.

On the first floor of House on a Hill, another row of bay windows contains the bedrooms and a study, stepped back from the lower level to create more private-feeling balcony terraces.

Extensive shelving, picture rails and nooks allow for the display of a large collection of objects and books throughout these spaces, integrated above deep, striped wood panelling and within window sills.

A spine of service spaces, such as the kitchen, bathrooms and the apartment's lift and stairs, runs along the northern party wall. Coloured circular skylights pull daylight into the stairwell and a shower.

Externally, the entire home is clad in vertically laid dark plum-coloured bricks with contrasting pale mortar, chosen to nod to the surrounding brick buildings while remaining distinctive.

House on a Hill was completed by David Kohn Architects for developer Baylight Properties. Other projects by the studio include the Gradel Quadrangles in Oxford, a sinuous, stone-clad building containing student accommodation and a tower of offices, and a home in a converted cowshed that celebrated its "agricultural identity".

The photography is by Will Pryce.