I am wondering if William Wicken Verral's father could have been William Wicken Verral as well . . .
It looks as if William Wicken/Wicking Verrall's middle name was his mother's maiden name. William Verral, bachelor, and Alicia Wicking, spinster (both of Trinity district, St Marylebone) were married by banns on 10 November 1833 at Trinity Church, St Marylebone. He marked and she signed. Witnessed by Hannah Baugham (or Bangham?) and Henry Charles Bell.
Alicia must have died not long after the 1841 census: she is recorded as dead when her daughter Alicia was baptised in 1842.
Could this be William snr in 1851? All children born St Pancras
St Pancras, HO107; Piece: 1493; Folio: 139; Page: 31
William Verrel 38, Carman and Coal ?????, Horne Surrey
Elizabeth Verrel 35, Wandsworth
Richard Verrel 13
Jesica Verrel 12
George Verrel 3
John Verrel 1
That looks good, Mealymoo.

There was a Richard in 1841 if I remember correctly, and maybe Jesica is Alicia junior in disguise [the enumerator put her name down as Louisa at first, but then crossed it out]. The big gap between those two children and little George (3) and John (1) might indicate that William had remarried fairly recently.
This might fit with a marriage on 23 May 1847 at St Pancras: William Verrall junior, full age, widower, a porter of Miller Street, son of William Verrall, labourer, married Elizabeth Ann Stiles, full age, spinster, of Caroline Street, dau. of Henry Stiles (dead). Both made their marks. Witnesses J(?) Dutton(?) and S(?) Verrell.
Edited to add: ah, yes: just noticed that they were in Miller Street in 1851 so that all seems to fit.
So to confuse things the one we were calling William senior (who married Alicia) was calling himself William junior at the time of his 2nd marriage in 1847, suggesting that his father William was also around at this time.