"Vilikins" = "Wilkins", believe it or not. In the cockney of Dickens' time, V and W were switched, so "very white" became "werry vite" (phonetic spelling!). Also, comic songs (and sea shanties) tended to insert extra syllables, whence the intrusive second "i" in Vilikins. The first line of the song (by the way, I think it was by Mark Sheridan, but I may be completely wrong!) goes "It's of a rich merchiant this story I tell". Let's see how much I can remember ...

It's of a rich merchiant this story I tell,
Who had but one daughter, an uncommon fine young gel,
Whose name it vas Dinah, just sixteen years old,
Vith a werry large fortin [fortune] in silwer and gold.
Singing ... [there is some patter before each chorus, which I've forgotten]
Too-ra-lie oo-ra-lie or-ra-lie-ay.

[Switch your own v's and w's from here!]

Now, as Dinah was a walliking [walking] in the garding one day -
{spoken] it was the front garding -
Her father came to her and to her did say:
"Go dress your self, Dinah, in gorge-i-ous array, I will find you a husiband both galliant and gay."
Singing ...

"Oh father, dear father," young Dinah replied,
"I don't feel inclined for to be marri-eyed,
And all my large fortin I'd gladly give o'er
If you'd let me stay single a year or two more."

[verse missing]

Now, as Vilikins was a walliking in the garden one day -
[spoken] it was the back garden -

... and now it's gone completely, I'm afraid; except for the end of the last verse:
With a bill-dow what said as how by pizen [poison] they died.

"Billy-dow" = billet-doux (French) meaning a love-letter (not a French letter!). It's basically Romeo and Juliet in modern dress, but with more jokes. Actually, the last verse is not the final one; there was a "morial" (moral), and there were two extra morals added, I suspect through public demand. The first morial is that this is what happens when you go against parental orders; the second is that this is what happens when parients (sic) go against the hearts of their children.

Steve