So I went & listened to MacColl's version. Very different set of verses from the usual but he includes the following:

Just take a trip to Liverpool, To Liverpool, that packet school.

There's Liverpool Pat with his tarpaulin hat, And Paddy McGay, that packet rat.

So I guess with that and with the info that 14 knots would be extraordinary for a packet ship but not for a clipper (Thanks All), I guess the song most likely originally refers to the 1817 packet line. Although, obviously it could have been used on both.

Barry - you too. We're certainly moving to NC within the year.

Grab - Seems it wasn't unusual for a sailor to get drunk, rolled and wind up nearly naked. Sometimes naked and Shanghaied. (Maybe he'd find all he had left was: "...an old suit of oilskins and two pairs of socks / And a bloomin' great head and a dose of the pox."

Others would (apparently) not bother to bring any gear, intending to steal what was needed from other sailors. Officers might (or might not) be ordered to watch out for such lowlife and not let them on board without their own kit. A Dutchman might be an easier mark or less sympathetic or just that the Anglo sailor might be able to get away with bragging about this but the others might object to him stealing from another Anglo sailor.

That (from your verse) would be the 1817, the packet line. It only sailed from NY to Liverpool. And back.