Museum of Archaeology/Peterhouse Library - Little St Mary's Lane, Cambridge, UK - Architecture Prizes on Waymarking.com

The building is Grade II listed with the entry at the Historic England website telling us:

Museum of Classical Archaeology. 1883. By Basil Champneys. Ketton stone arcade with red brick filling 8 bays, the entrance being in the last on the right. Plinth supporting plain Ionic half-columns paired at either end; entablature with dentils, balustrade with vases on the columns and an extra one over the door. The doorway has freestanding Ionic columns topped by lions supporting arms, coat of arms in centre, double doors. Roof not visible. In the South wall, facing onto Peterhouse is the remains of a C16 4-centred arch end brick wall. Plain interior. Apparently converted from existing warehouses connected with the port. Some features remain, cellars, timbered roof, entrance ramp, hoist etc. A clever conversion for existing use.

The Cambridge Museum History website tells us about the Museum of Classical Archaeology at this location:

The Museum was originally housed in a building belonging to Peterhouse College in Little St Mary's Lane, known affectionately as 'The Ark'. This building, however, was only leased for one hundred years from the college – and, as the end of the lease fast approached, a new home for the casts had to be sought. In 1983, the casts moved into their present home, a purpose-built Cast Gallery in the Faculty of Classics on Sidgwick Avenue. For the first time, the Museum of Classical Archaeology and the Faculty were united under the same roof.

The Peterhouse College website tells us about the Ward Library at this location:

The third of our collections is the Ward Library – the undergraduate working library of some 60,000 volumes, which opened in 1984 in the building in Little St Mary's Lane that, for a hundred years, had housed the Museum of Classical Archaeology. The Library takes its name from Sir Adolphus Ward, who was Master from 1900 to his death in 1924. Until his death, all the College's books had been housed in the Perne Library, the cases of which had been built up and adapted over the centuries to take them. Ward left some 5,000 volumes to the Library – chiefly of English literature and English and foreign history. They were too many to fit into the Perne; and so his bequest precipitated the foundation of a library designed specifically for the working requirements of undergraduates. For the first thirty years of its existence it was housed in Burrough's Building – first in one room on the first floor, and eventually taking up both first-floor sets – which provided both a bookstack and a reading room. The Perne Library, having been reduced to proportions which could be accommodated largely in the original cases, reverted to being a scholars' library, and was open only for the purpose of research. In 1952, however, the growth of the Ward made another move imperative. The Ward books were now moved to the attics of G staircase, and the Perne Library was reopened as a reading room.

Wikipedia has an article about Basil Champneys that tells us:

Basil Champneys (17 September 1842 – 5 April 1935) was an architect and author whose most notable buildings include Manchester's John Rylands Library, Newnham College, Cambridge, Mansfield College, Oxford and Oriel College, Oxford's Rhodes Building.

Champneys was born in Whitechapel, London, on 17 September 1842 into a family with a modest income, his father, William Weldon Champneys, was an Evangelical Vicar of St Mary's Church, Whitechapel (later Dean of Lichfield). One of eight children, he attended Charterhouse School, showing a talent for mathematics and lacking in drawing skills. In 1860, he entered Trinity College, Cambridge. In 1864, he failed to get the 'first class' degree he had hoped for, achieving a second class in the Classical Tripos, and he took articles to study as an architect with John Prichard, the Surveyor of Llandaff Cathedral. Champneys set up his practice as an architect in 1867 in Queen's Square, London, close to the office of William Morris & Co.

In 1876 he married May Theresa Ella, a daughter of Maurice Drummond, descendant of William Drummond, 4th Viscount Strathallan, and they had two sons and two daughters. Champneys was a member of the Century Guild, the Athenaeum Club and the Saville Club, making acquaintances with Walter Pater, Robert Louis Stevenson, Sidney Colvin, and Coventry Patmore. In 1912 the Royal Institute of British Architects awarded Champneys its Royal Gold Medal for architecture. Champneys died at his home, 42 Frognall Lane, Hampstead, on 5 April 1935. He was the brother of Brasenose rowers Weldon Champneys (clergyman) and Sir Francis Champneys (doctor).

His writings include an introduction to Henry Merritt: Art Criticism and Romance, published in 1879 and Churches about Queen Victoria Street, a portfolio published in 1871, Victorian art and originality for the British Architect published in 1887, and The architecture of Queen Victoria's reign for the Art Journal, published in 1887. A Quiet Corner of England was published in 1875 after being circulated as a portfolio and a work regarding his mother-in-law, Adelaide Drummond, A Retrospect and Memoir, was published in 1915. Champneys' correspondence has been preserved in the General Collection of the Beinecke Rare Book and Manuscript Library.

Believing that architecture was 'an art not a science' he joined the Art Workers Guild instead of the Royal Institute of British Architects. Although Champneys was able to work in the Gothic style that John Prichard preferred and taught, he later became one of the pioneers of the Queen Anne style, working on at least 100 buildings throughout England. John Rylands' widow, Enriqueta Rylands, had admired the library Champneys had designed for Mansfield College, Oxford and hired him to develop the design on a more lavish scale – The John Rylands Memorial Library in Deansgate, Manchester took nine years to build before opening on 1 January 1900, it is one of Champneys' finest designs.

Champneys' Oxford buildings include the Indian Institute (1883–1896), Mansfield College (1887–1890), the Robinson Tower at New College (1896), The Rhodes Building in Oriel College (1908–1911), Merton College (1904–1910), the library of Somerville College (1903) and the Church of St Peter-le-Bailey (1872–1874), which serves as the chapel for St Peter's College.

His Cambridge works include the Archaeological Museum (1883), now Peterhouse Theatre, the Divinity and Literary School and Newnham College (between 1875 and 1910), for which he is credited for bringing a 'touch of lightness' to the college and is acknowledged for his attention to both construction details, and to cost.

Champneys' buildings elsewhere include the chapel of Mill Hill School, London (1898), buildings for Bedford College in Regent's Park (1910), King's Lynn Grammar School, Norfolk (1910–1913), the Butler Museum at Harrow School (1886), the museum at Winchester College (1898), and Bedford High School (1878–1892).

Churches by Champneys include his father's parish church, St Luke's, Kentish Town (1867–1870), the sailors' church of St Mary Star of the Sea, Hastings (1878), and St Chad, Slindon, Staffordshire (1894). In 1897 he did the painting of clouds, cherubs and scrolls on the ceiling of St George the Martyr Southwark in London. In 1898 he added a porch to St Mary, Manchester, where he was surveyor, and between 1902 and 1903, a south annexe. His home, Hall Oak, in Frognal, Hampstead was also one of his works.