I thought that the song really needed to be longer, giving people another chance to join in the excellent chorus. I'm sure Hughie Jones would have written more verses, but decided on the three we have. Researching the Wavertree's history on the www gave me enough material for an attempt at stretching (many would say padding) the story, and for better or worse I've come up with the following.
THE WAVERTREE
(Hughie Jones)

When I was small at me grandad's knee he'd sing his auld songs and he'd yarn to me
Of sailing ships and years long past, and serving time before the mast.
Sometimes a faraway look would come, I knew I'd be hearing a special one;
Of every ship, on every sea, his favourite was The Wavertree.

  Chorus:
  Running your Easting down, 
  Running your Easting down.
  Ain't you proud to be signed AB
  On a Liverpool ship, The Wavertree,
  Bowling along in a Westerly.
  Running your Easting down.

A full-rigged ship, two thousand ton, Southampton built for the Calcutta run.
When demand for jute began to fade she entered the Australia trade.
In later years her cutback crew humped dirty cargo off Peru.
When steam beat sail eventually, they damned near starved in Wavertree.

  Chorus

For twenty-five years she played her part 'til a Cape Horn snorter broke her heart.
Dismasted, too far gone to save, bound for a South Atlantic grave.
A storage hulk in Magellan Strait then a sand barge on the River Plate
Til a man who loved tall ships at sea searched and found the Wavertree.

Chorus

They towed her to a friendly shore last seen over seventy years before
Almost forgotten, tired and worn, but the old windjammer's been reborn.
If grandad were alive today he'd not believe it if you'd say
A century on a New York quay would berth his favourite Wavertree.

  Chorus
  Running your easting down.