Amelia Uden was born on a farm in Hadlow, Kent, surrounded by orchards and animals. Both her parents were artists and she attended Reigate and Redhill School of Arts and Crafts where her father taught full time. Here she studied weaving with Morfudd Roberts (who had succeeded Elizabeth Peacock), moving to Chelsea School of Art in 1965 for the textiles Dip.AD course but returning to Reigate to attend an evening class in chemical dyeing. From 1968 to 1971 she was a student at the Royal College of Art under Marianne Straub, whose support she received for the rest of Straub's life. In her last year, Uden won an RCA Travel Scholarship to study the Lyons silk weaving industry.
On graduating, Amelia Uden worked for William Hollins and Co (Viyella), Nottingham, as a designer directing sample-weavers in Glasgow; this was an unsatisfactory period for her. She resolved to be a maker on her own account and returned home to Kent to set up and operate her own workshop in 1973, aged 27, while concurrently teaching at Horsham School of Art. The original loom she used was a shaft drawloom but on a visit to the expert drawloom weaver Alice Hindson in 1975, whose own 'Aladdin' drawloom was for sale, she purchased it and later spent over a year re-building the harness. She continued to correspond with Hindson until her death in 1984. Uden wove silk lengths and samples full time for four years (1978-81), working to commission and for public collections. In the period she also moved to Suffolk and received an Eastern Arts Major Award enabling her to continue to concentrate on drawloom research and weaving.
In 1981 her work attracted the attention of Margaret Bide, Head of Textiles at Farnham School of Art (now the Surrey Institute of Art and Design, University College) who purchased pieces for the college's collection and invited Amelia Uden to be external examiner there. Following that, she became increasingly involved in textiles education at Surrey Institute and was appointed part-time lecturer in 1984 and subject leader in 2001. She moved her home and workshop to Farnham in 1991, where she continues to live, teach and weave.