"William Andrewe, of Deinton, alias Little Doddington, co. Northampton, esq" was created baronet 11 Dec 1641, says Cokayne. No doubt for the usual services to the cash-strapped King.
So the baronetages have no clue who the 1st Bart's father was.
The VCH Northants article on Denton confirms that this parish was also called Deinton or Little Doddington, the names in the patent. It goes on to mention a "William Andrews" whose wife Frances came into the property of her father Sir John Flamstead in 1632.
This is clearly the same "William Andrew of Denton" who appears in the 1618 Visitation of Northants (ed. Metcalfe, self-publ, 1887) p. 66. TIf correct, this would appear to solve the problem of the baronet's origins, making him the younger son of an Andrew of Harleston, they being a cadet branch of the Andrews of Charwelton. And presumably it's correct, as William's eldest son was 4 at the time.
The puzzle is why the connection wasn't made by VCH or the baronetages.
Sir William's wife as shown by Cokayne doesn't match Vis. Northants, but could be confused, as the same description "__ da. of __ Paris" is given by Cokayne for the mother-in-law of Sir William's son, Sir William (3rd Bt). This evidently comes from Vis. Essex, Vol. 1, ed. Metcalfe, Harleian Soc. 13 (1878), p. 337 (Atslow, 1634). (Note this chart has been updated since the Visitation - the baronetcy didn't exist in 1634)
__________
Have you taken a DNA test? If so, login to add it. If not, see our friends at Ancestry DNA.