The genre of music is Trip Hop, it's an experimental form of breakbeat that incorporates Jazz, soul, hip hop and ambient sounds. Their album Dummy is fantastic, it actually features on rolling stones list of greatest albums of all time. Another great trip hop group is Massive Attack who are from the same part of the UK. The closest thing you have got to trip hop your side of the pond is probably DJ Shadow whose music I also love, he did a lot of instrumental hip hop.