I couldn't find a copy of the 1881 edition of the Lloyds Register of Shipping online (it's possible that your local reference library may have a copy). The nearest volume that I could find is the 1883 edition which has been scanned and made available on Archive.org.
Unfortunately, there doesn't seem to be any ship named Bancroft listed in that year.
Some points to note about the Lloyds Register. Since 1875, Lloyd's Register has included all British vessels of 100 tons and over, whether or not they had been surveyed and classed by Lloyd's. Also, until 1890, Lloyd's Register was almost exclusively confined to British registered vessels.
This suggests that the Bancroft was either a small vessel, under 100 tons, or a foreign-registered vessel.
It is quite possible that she was a barge or a small fishing vessel. This list is dedicated to "Canal People" and suggests that the Bancroft might have been a barge, however I'm not sure how reliable that is.
It is worth checking with the local archives in the area to see whether any have lists of 19th century barge registrations. As master, I believe that Joseph would have had to be registered, but I think this was a local register for a particular canal, rather than a national one.