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Designed by Michael Hopkins & Partners, the £35m extension to the rear of Manchester's classical art gallery is a perfect fit.

Before the extension was built, the gallery comprised two free-standing stone buildings designed in the classical style by Charles Barry, the architect of the Palace of Westminster. In contrast, Hopkins' atrium linking the two buildings is overtly and unfalteringly high-tech. Walls, roof, balustrading and the treads to the stairs are all in clear frameless glazing, whereas handrails and fixings are polished stainless steel. Yet so perfectly judged and superbly refined is the modern extension that it fits into its classical parent buildings as naturally as fresh flowers in an antique vase.

How has Hopkins pulled off this architectural coup? For a start, the clear glazing and minimalist detailing and structure – all hallmarks of his high-tech style – present the least physical interference with the historic buildings. The freshly restored stone ashlar facades and ornately carved cornices of the classical galleries continue without interruption through the new atrium, as if they remained detached buildings instead of newly linked ones.

In addition, the new elements within the atrium have been arranged and detailed with classical symmetry and simplicity. The staircase has been aligned on the central axis of the main front block, and in a similar manner to Barry's central staircase in the original gallery, it takes the form of a double spiral that feeds into the two rear wings on either side.

One of the two rear wings is also new and completes the city block. It is a demure box with flat sides and roof, and it has been articulated in the classical manner with a plinth, middle and cornice. Needless to say, these are impeccably modern and functional in detailing. Even the stone ashlar, taken from the same quarry as for Barry's buildings, is expressed as modern, mechanically fixed cladding panels bounded by shadow gaps.

Hopkins' gallery extension, to be opened on 25 May, combines contemporary self-confidence with a gravitas and composure to match their classical neighbours. Compared with most lottery-funded projects, which strive to become icons through brash effects, it is a refreshingly pure change.