Hi Lee
Thanks to you and others who have kindly contributed, I think together you've managed to open a 'dead-end' with Thomas Beck b.1815 in Ulveston by identifying Nancy Beck as his likely mother and very possibly her parents too. Well done! Myself and others have been unable to go further back than Thomas until now. His naming a daughter Nancy is obviously a big clue as are the parents of Nancy being a Thomas and Agnes. Agnes is a name that was regularly changed to Nancy so I've just discovered so this may increase the possibility further.
The marriage of Nancy Beck to Ratcliff Wrigley is also new to us and the latter Wrigley / Beck census connections are worth exploring. As is the likely 1871 Richard 'Beck' (Greenhalgh nephew) and I will look into this when I subscribe to Ancestry shortly.
In terms of Patience Greenhalgh's parents and also the Squire Greenhalgh witness connection, there seems to be a gap in the St.Mary The Virgin (Deane, Bolton) Baptismal Records for 1813-1821 when I suspect either Patience or Squire may have been baptised. It would be useful to know if these records simply no longer exist or if they have not yet been transcribed are unreadable? Any help that anyone can offer on that mystery would be great?
Unfortunately to complicate matters the combination of names; Squire and Greenhalgh seems to be very popular within the Greenhalgh family locally according to a general Lancs OPC search, so it is not quite as unique as it might sound. So it's not immediately obvious whether this Squire is a sibling, parent or even a cousin or uncle of Patience at this stage. But interestingly this record of their apparent first born son gives an indication of its importance perhaps and where we should be looking (squire!):
Baptism: 15 Apr 1838 Horwich Chapel, Horwich, Lancashire, England
Squire Beck - Son of Thomas Beck & Patience
Abode: Horwich
Occupation: Cotton Spinner
Baptised by: David Hewitt, Minister
Register: Baptisms 1813 - 1841, Page 169, Entry 1351
Source: LDS Film 2113121
Going back further I've also spotted a Thomas and Charity Greenhalgh married in the parish around 1815 and they may have a connection in naming a daughter like the mother after one of the virtues; Patience. Tenuous link I know but perhaps one we might not want to discount at this stage. Albeit the name Greenhalgh is pretty much ramified in the area.
Marriage: 30 May 1815 St Mary the Virgin, Deane, Lancashire, England
Thos. Greenhalgh - Bachelor, this Parish [Deane]
Charity Kirkman - (X), Spinster, this Parish [Deane]
Witness: A. Boardman; Laurence Fisher
Married by Banns by: R Latham A.M. Vicar.
Register: Marriages 1813 - 1818, Entry 59
Source: Manchester Archives microfilm