Family Search has added transcripts of the 1871 England and Wales Census to its database. It's not quite complete yet, but with more than 81% of the total now available, it's worth checking out.
In 1871, there were 605,282 Irish-born individuals living in England and Wales (a further 207,820 were in Scotland). The largest concentrations were found in London (91,100), Liverpool (76,700) and Manchester (34,000). The numbers make clear why this is an important collection for Irish family historians to search for 'missing' ancestors, whether they subsequently returned to Ireland, settled in the UK or emigrated, typically from Liverpool, for the United States.
While images are not provided by FamilySearch (there's a link to FindMyPast to view them with a subscription), the FamilySearch transcriptions contain all the information provided on the census forms for each individual: name, age, marital status, relationship to head of household, occupation and place of birth, as well as listing name, age and place of birth for all other occupants of the household.
The majority of the census records do not say where in Ireland the individual was born, but for some lucky researchers, the name of the county is recorded.
Note: All stats from The Irish In Britain 1800–1914, by Donald M MacRaild; 'Studies in Irish Economic and Social History' series.