Greenwood became a full member of the Royal Society of British Artists in 1922, and exhibited at the Royal Academy 1920-1933, the Royal Institute of Painters in Watercolours and the Royal Society of Portrait Painters, as well as widely across London at Colnaghi, Beaux Arts Gallery, The Groupil Salon Gallery, and the Leicester and Grosvenor Galleries. A centenary exhibition was held at The Bloomsbury Workshop in 1992.
Greenwood completed iconic poster designs for the London Underground and the Great Western Railway, and designs for London shops such as Liberty and Whiteleys.
His works can be found in numerous public collections in the UK including Manchester City Galleries, Towneley Hall Art Gallery & Museum, Harris Museum & Art Gallery and Grundy Art Gallery.
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