Broken beat is an electronic music genre that is characterized by syncopated rhythm typically in 4/4 meter, with staggered or punctuated snare beats and/or hand claps. It first appeared in the 1990s and was pioneered by IG Culture, and the release of the 4hero album Two Pages was influential on the emerging sound and scene. Appearing in the western parts of London, the genre is also referred to as West London, mainly because Goya Music's offices were in London's Ladbroke Grove, W11, as were most of the participating artists studios. Artists in this area mostly have a drum and bass, house, hip hop, techno or acid jazz background.
Nu jazz is an umbrella term coined in the late 1990s to refer to music that blends jazz elements with other musical styles, such as funk, soul, electronic dance music, and free improvisation. See Wikipedia for more info on Broken Beat and Nu Jazz.