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Now that old modernism has been reinstated as the new orthodoxy, buildings that revert to the classical style are regarded as weak-kneed – and in a historic setting such as Oxford, obsequious. One glimpse of the £14m Sackler Library for Oxford University is enough to sweep away such notions. For a start, this is a big building: a bold five-storey drum that towers over a Georgian terrace. In fact it is (the architect claims) the largest classical public building in Britain for 30 years.

It was designed by Robert Adam, the most vociferous of Britain's classical architects. Adam likes to call his approach "21st-century classical architecture". His Sackler Library can be read as a case study of the potential – and pitfalls – of classical design in the 21st century. Externally, it works remarkably well. From the surrounding streets, only parts of the building are visible, but a glimpse of the main library rotunda is enough to provide the viewer with a sense of its entire volume.

The circular geometry is echoed in miniature in the drum-shaped entrance hall, which is decked out in full doric regalia borrowed from the temple of Apollo at Bassae in the Arcadian mountains. This is all the more appropriate, as it was the inspiration for Victorian architect Charles Cockerell's Ashmolean Museum.

The building's interior keeps up the architectural momentum: so much so that the classicism shows signs of unravelling. The complex of blocks and courtyards cries out for a clear axis culminating in a grand double-height space in the library rotunda. Instead, the entry sequence has been dissipated in complicated cross-axes, and the rotunda turns out to be a layer-cake of congested single-storey spaces.

Within the rotunda, the bookstacks make up the core of each floor and are bracketed by four hefty doric columns at each corner. Chunky oak and leather desks and chairs have been purpose-designed by Adam in Greek classical style.

But a closer look reveals the array of out-of-style details and fittings that intrude on the classical scene. These include square-edged ceiling recesses next to ornate ogee mouldings, plastic D-handles on the doors, recessed light fittings, commercial carpet tiles and, much to Adam's chagrin, card-operated security gates.

The doric columns in the library beg the visitor to test them out – knock on them, and they emit the tinny sound of a false metal casing.