Garner was almost exclusively responsible for the design and supervision of most of the work at Oxford, including the alterations and tower at Christ Church, St Swithin's Quadrangle and the High Street Entrance Gate at Magdalen College, and the Master's Lodgings at the University College. He was entirely responsible for the subsequent President's Lodgings at Magdalen College.
Garner was the primary architect responsible for a large number of projects at Oxford, including renovations to existing buildings like Christ Church and St Swithin's Quadrangle, as well as new constructions such as the High Street Entrance Gate at Magdalen College and the Master's Lodgings at University College. He also had sole responsibility for the construction of the President's Lodgings at Magdalen College.