Loo,
The forenames don't sound Jewish to me but then, I'm no expert.
They are :
William b approx 1788 married Ann, both from Westminster, Middlesex with children William (tailor, b1818), Mary(1828), Sarah(1828), Martha(Dressmaker, b1832). Probably more offspring but not found them yet.
Then William (1818) married Ann Faith and had children ...
Jane (tailor, b1840), William(1841), Ann(tailor, b1847), Mary (tailor, b1849), Martha(domestic, b1851), George (stuff warehouse boy,b1855), Thomas (stuff warehouse boy, b1857), Charles (traveller then unionist registration agent !!, b1859), Betsy (1862)
It is this family that moved around between Yorkshire and Middlesex.
Ann Faith's parents (William and Jane) were both Tailors from Stockton, Durham.
As I said, names don't seem Jewish.
But when I looked at the surname on the link you posted, Levitt is either Jewish (Levy derivative) or English (Leavitt derivative).
But there were not many Leavitt families in England and they showed no tendancy toward being tailors.
Whereas Levit/Levitt/Levy is much more common (especially Levy) and clearly a lot of tailors.
So - the jury is out !
Any ideas much appreciated.
Cheers
Bev