1851 HO107; Piece: 1479; Folio: 565; Page: 25
has Richard Judd living with Frederick. Richard is born Warwickshire.
That doesn't help much I know

However I notice that in 1851 they have younger children so you could send for a birth certificate to get Sarah's maiden name and then take it from there.
You also say that John moved to London but he gives his birthplace as Middlesex (Soho I think on one census)
best wishes
heywood