Hi Jen,
I've looked at my DB on Suffolk millers just for Beardwell. It has thrown up the following:-
1743/03/05 pg.4 c.1 "To be LETT, and enter'd upon at Lady-Day, or Midfummer next, at STRATFORD in SUFFOLK.
TWO very good WATER-MILLS, one of which is employ'd in the Oil Bufinefs, the other in the Corn; with a Dwelling-Houfe belonging to each; Alfo Grainaries, Out-houfes, and all Manner of Conveniences; the whole in very good Repair, lately in the Occupation of Mr. JOHN BEARDWELL, deceas'd, and now occupied by his Widow.
For further Particulars enquire of Mr. Samuel Todd, Grocer, at Head-Gate, Colchefter."
1756/11/30 pg.5 "THE creditors of John Beardwell, of Stratford in the County of Suffolk, Oylmiller, are defired to meet the faid John Beardwell, at the Swan Inn in Stratford aforefaid, on Monday the 20th Day of December, at Eleven of the Clock in the Forenoon, to confider of Propofals for affigning over the faid John Beardwell's Eftate and Effects, for the Payment and Satisfaction of all the faid John Beardwell's Debts."
This is a water mill, long gone, at Stratford St. Mary.
I have nothing (yet) on your later John Beardwell, but it is an unusual name, and milling ran in families so they are likely to be related.
If I find anything else I'll forward it on to you.
Happy hunting,
Windy Miller
PS. I'll add your chap to my DB. Thanks. If you get anything else I'd appreciate being able to add it too.