In the history of decorative arts, textiles operate according to their own laws. Sometimes they lead fashion; sometimes they follow. Some have the names of famous artists attached as designers, but some of the most attractive and original designs may be anonymous. To test this assertion, visit the current series of exhibitions at Francesca Galloway in Dover Street, a specialist dealer known for her expertise in Islamic textiles, but now taking the lead in the scholarly display and documentation of 20th-century designs.

‘Neo-Classicism to Pop: European Textile Design 1790?1970′ is a rotating collection of original woven and printed patterned lengths, printers’ ‘fents’ (sample prints on paper), and original designs. For newcomers to this field, it would be an ideal introduction to a range of styles and techniques, linked to a diversity of pattern designs that charts the emergence of a modern style from the Arts-and-Crafts movement. It is very rare to be able to see so much in one place, and at such close range: Marion Dorn, Wiener Werkståtte, Lucienne Day, Raoul Dufy and Paul Poiret are all represented names to whet the appetite of the existing enthusiast. The collection has taken years to assemble and research, and most of the pieces will probably find themselves in museums around the world. In addition, there is a sumptuous but very informative and readable catalogue, in two volumes, written by the textile historian Sue Kerry. France was at the centre of fashion trends, and represents at least half the items.

The traditional silk-weaving skills of Lyon and the textile printers of Alsace were stimulated by fresh designs from the School of Paris, represented above all by Dufy, a painter of talent but a designer of genius, who reinvigorated the Toile de Jouy practice of light hearted pictorial design. The large decorative arts exhibition held in Paris in 1925 was a moment when parallel trends in design could be observed, some deliberately neo-primitive, like the bright flowers of Bégonia by Atelier Martine (a branch of Poiret’s enterprise) or the filigree shimmer of Les Chrysanthèmes by Maison Henry Bertrand. These styles remained current until the end of the war, as evidenced by Lyre Bird and Tropical Foliage, produced by the Lyons firm of Bianchini Férier in 1944 for the liner Maréchal Pétain (soon to be renamed La Marseillaise).

The remainder of the exhibition is predominantly British, beginning with a fascinating curiosity, a plush fabric block printed with a swirling design by the architect C. F. A. Voysey and marketed in the US for first-class railway carriage seating. A group of designs by Alec Hunter for the St Edmunds-bury Weaving Works shows the transition from historical tradition to Modernism, including a sample of the binding cloth woven for the None such Press edition of George Herbert’s The Temple, which matches the 17th-century period of the poems in its imagery and tactile feel.

Few individuals were more important for linking British craft workshops to Modernism than Marianne Straub. She came from Switzerland and obtained Government backing to work with 72 Welsh woollen mills in the 1930s, creating designs in which the structure of the cloth relates to the simple pattern. A matching pair of striped curtains, marketed by Gordon Russell in 1935, was actually hung in Russell’s own house. Although interwar design aspired to sophisticated simplicity, the war induced a patriotic jollity, with a Courtauld dress fabric, Dig for Victory, 1941, made up of vegetable seed packets, and a Victory headscarf, with the flags of the four allies.

The jollity continues into the Festival of Britain, with Lucienne Day’s classic design Calyx, used in the Homes and Gardens pavilion and a subsequent bestseller, but there are more of her designs, together with classics by Jacqueline Groag and Marian Mahler, two other notable émigrés, before the mood darkens dramatically with the superb Whithorn, by the painter William Scott, commissioned by the architect Eugene Rosenberg for the Altnagelvin Area Hospital in Northern Ireland, and Legend by Alan Reynolds, based on an abstract painting. Then colour breaks out again in the 1960s, bringing the sequence to a close with bold bright patterns that, despite their relatively recent date, are as much rare exotics as their predecessors. ‘Twentieth Century Textiles’ is at Francesca Galloway, 31, Dover Street, London W1, until July 14 (020?7499 6844; www.francescagalloway.com)