One example of this is Raoul Dufy, who in the 1910's was commissioned to design textiles, with people such as Paul Poiret being drawn to his primitive, folk-art quality wood cuts, overlapping and juxtaposing of layers, stylised designs and pure colours. I love the way his pieces suggest movement and excitement.
A group of artists that also shared this belief was the Omega workshops, set up in London by Roger Fry in 1913. The aim was to destroy the distinction between fine and applied, by working on objects, textiles and furniture. The co-operative ran for 6 years but continued to be influential for a number of years after, with their abstract, colourful designs. I have been drawn to their work after learning about it at A-Level, as I admire their mission and love the colour palettes used in the work.
1. Raoul Dufy for Bianchini-Ferrier, Fashion textile Charlot, block printed silk, c.1919
2. The Omega workshops textiles swatches, 1913, linens
Both images from 'Artists' textiles 1940-1976' by Geoff Rayner.