I have many, many Irishmen (and women ) in my family, as my mother's side is almost fully Irish. A lot of our family immigrated here from Ireland by ship, BUT the ships often (almost always!) would stop over in England after departing from Ireland.
I've found a number of my family members who left the ship during the stop over in England, and some never reboarded (while others did). Those who made it to Canada were relatively easy to find with some research, digging for clues, and doing a bit of "detective work."
For those in my family who did not reboard vessel after the stop over in England most likely went on to find work there and establish a more secure and stable life. For those individuals, I had to go do my research using England's various databases, libraries and archives (including vital statistics, census', marriage certificates, birth & death records, gravesite searches - it's best to start with the free national website called "Find A Grave" for that one!).
There's also many ship and vessel databases available that you can search online, most of which offer valuable passenger lists that usually include names, ages, ethnicity, ports of origin/departure, ports of embarkment, # ppl in each group/party (i.e. alone, a couple, a family of 5, etc.).
Some vessel and passenger lists are more detailed, while others offer much less information. It's an excellent resource for genealogical research, particularly if you have a good idea of where your ancestors came from (Ireland), and where they embarked from their long journey at sea (New Brunswick, Canada - most likely in a major port region/city at that time, which there weren't many of back then!).
Perhaps they even got off the ship in Nova Scotia, in a major port city there rather than in New Brunswick, and then made their way to NB to settle. Let's keep in mind, of course, that many Canadian city names in have changed since the 1800s, especially in Nova Scotia.
I have numerous reliable, verified, free online resources for such research bookmarked and written down in my notes. I'll try to comb through my family genealogy files and hopefully update this reply with some of those links!