Born in 1932 in London, Uglow inherited his tutor's (William Coldstream) system of measurements and marking, preferring to paint nudes and still lifes, and depicting them almost sculpturally. He showed the making of the piece in the painting itself, delineating each plane precisely. In a continuation of this geometrical obsession, Uglow liked his canvases to be a golden rectangle, a square, or rectangle of exact root value.
Uglow attended Camberwell School of Art from 1948 to 1950, where the tutors included John Minton, Victor Pasmore, and William Coldstream. He was greatly influenced by the latter, as well as by Claude Rogers. When Coldstream left Camberwell for the Slade, Uglow followed him, studying there from 1951 to 1954. When he left, he undertook community work in lieu of military service, having registered as a conscientious objector.
In 1961, Uglow taught part-time at his two alma maters, and thereby continued a lifelong association with the Slade. He turned down an offer to become a member of the Royal Academy in this year and had his first show at the Beaux Arts Gallery. Uglow had an exhibition at the Whitechapel Art Gallery in 1974 and then showed at Browse & Darby until the end of his career. He also showed in the US, in Jerusalem, and at many prestigious galleries in England. In 1991 he became a trustee of the National Gallery. Uglow died in 2000, at his home in Wandsworth.