The Irish Travellers are a population with a history of nomadism; consanguineous unions are common and they are socially isolated from the surrounding, 'settled' Irish people. Low-resolution genetic analysis suggests a common Irish origin between the settled and the Traveller populations. What is not known, however, is the extent of population structure within the Irish Travellers, the time of divergence from the general Irish population, or the extent of autozygosity. Using a sample of 50 Irish Travellers, 143 European Roma, 2232 settled Irish, 2039 British and 6255 European or world-wide individuals, we demonstrate evidence for population substructure within the Irish Traveller population, and estimate a time of divergence before the Great Famine of 1845-1852. We quantify the high levels of autozygosity, which are comparable to levels previously described in Orcadian 1st/2nd cousin offspring, and finally show the Irish Traveller population has no particular genetic links to the European Roma. The levels of autozygosity and distinct Irish origins have implications for disease mapping within Ireland, while the population structure and divergence inform on social history.