Hi
It may be insignificant, given that Walker is such a common name, but the Leeds Mercury for June 24th 1815 carries a report of a trial of some men accused of stealing 12 bushels of wheat and eight of malt from Samuel Walker, maltster 'of this place' i.e. Leeds.
The Sheffield Independent for August 21st 1830 carries a notice of marriage: 'On Thursday week at Leeds, Rev Wm Pemberton, Wesleyan Minister, Dudley, to Marianne daughter of the late Samuel Walker, maltster of that town (i.e.Leeds)
If you could find a will for a Samuel Walker, maltster of Leeds who died between 1815 and 1830, it might either confirm him or rule him out as the father of Edward and James.
regards,
Lesley