He was born in Caim near Enniscorthy in County Wexford, Ireland and his surname suggests that he may have been a member of the German Palatine community that settled in the area in the early 18th century.
Some time in the mid-19th century, Heinrick moved to mainland Britain, first to Kirkcudbrightshire in Scotland and then to the Aston district of Birmingham, where he settled and worked as a schoolmaster.
In this work, he examined the lives of the Irish immigrants who had settled in mainland Britain in terms of their numbers, their occupations and their social and political status.
In 1874, a general election returned 59 MPs who were part of the Home Rule League, making it the third largest group in the British parliament at the time.
On 5 September 1874, ‘The Nation’ carried a report of a "complimentary dinner" to Mr Hugh Heinrick, Secretary to the Irish Home Rule MPs.