You have my sympathies!
Once you are back before 1837, it is worth looking at any records you can find: wills, manorial, deeds, poor law material and any catalogues and card indexes the record office may hold.
I don't know where Cockfield is in Suffolk, but Haverhill is near the border with Essex and Cambridge, so it's worth considering those counties too for stray references.
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The chestnuts cast their flambeaux
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