What is the relationship between the New Kadampa Tradition and Tibetan Buddhism?

New Kadampa Tradition is a prominent Buddhist movement in the UK with many centres and meditation classes. However I've always been confused about the relationship between them and Tibetan Buddhist. So moving on from this question - what is the relationship between the New Kadampa Tradition and the Tibetan schools? What lineage if any do they claim? Are they a minor school or a subset of another school? I heard somewhere that they had a disagreement with the Dalai Lamaso maybe they are linked with the Gelug school. However that might not be true - all kinds of things get reported about Buddhist organisations that can be classified as new religious movements, some of which are just sticks to beat them with.