The National Archives of England are accessible online.

I did a word search under the words “Caldwell” from 1000 to 1600, amd found 77 documents listed. A copy can be ordered and purchased.

The earliest document was a petition seeking recovery of a common pasture at Caldwell, Derbyshire, c. 1290=1307.:

Petitioners: The Town of Castleton of the Peak.
Addressees: King and Council
Places mentioned: Castleton, [Derbyshire]; High Peak, [Derbyshire]; Caldwell, [Derbyshire].
Other people mentioned: Brian de Lisle; William Peveril; John, King of England; Edward [I], King of England.
Nature of request: The petitioners seek recovery of their common pasture of Caldwell, which their ancestors had of the fee of William Peveril. They state that Brian de Lisle came in the time of King John and disseised them of the pasture, of which they had right of entry and exit from their common, on which they pastured their beasts without any gift and were seised from the time of William Peveril.
http://www.catalogue.nationalarchives.gov.uk/displaycataloguedetails.asp?CATID=-4411829&CATLN=7&Highlight=%2CCALDWELL%2CCALDWELL&accessmethod=0

A description of a Caldwell Manor is available, spelled Cawdwell.

SC 2/183/94 : Description of Courts: Manorial Courts.
Places: Rothley, with: Gaddesby; Baresbie; South Croson; Keyham; Somerby; Wartnaby; Grunston; Marefield; Tilton; Caldwell (Cawdwell); Wickham; Saxelby. 1, 2, 4 Edw VI. http://www.catalogue.nationalarchives.gov.uk/displaycataloguedetails.asp?CATID=6996950&CATLN=6&Highlight=%2CCALDWELL&accessmethod=0&Summary=True

SC 6/1107/14 : Burton-on-Trent (Lands of Burton-on-Trent Abbey): Stafford Branstone: Stafford Horninglowe: Stafford Stretton: Stafford Bromley [Abbots]: Stafford Ilam: Stafford Allestre: Warwick Mikleover (Magna Overa): Derby Winshill (Wynsull): Derby Stapenhill: Derby Caldwell: Derby Appleby: Derby London: [London] Description of Officer: Wardens. 33 Hen VI

I learned that at the time of the reformation, a Caldwell monastery, convent, and priory were dissolved. I am confused whether they are all at the same location or distinct locations.

SC 6/HENVIII/8 : Bedford: Monastic Possessions Possessions of the dissolved monasteries of:-- Caldwell, Harrold, Bushmead, Markyate. 27-28 Hen VIII.

SC 11/41L Caldwell, Markyate, Bushmead: Rentals of the Priory of Caldwell, the Monastery of the Holy Trinity in the Wood, and the Priory of Bushmead. [Hen. VIII?] http://www.catalogue.nationalarchives.gov.uk/displaycataloguedetails.asp?CATID=6702294&CATLN=6&Highlight=%2CCALDWELL%2CCALDWELL&accessmethod=0&Summary=True

E 25/26/2 : Caldwell, Beds; prior and convent of the Priory. 8 Oct 1534
http://www.catalogue.nationalarchives.gov.uk/displaycataloguedetails.asp?CATID=4265246&CATLN=6&Highlight=%2CCALDWELL&accessmethod=0&Summary=True

E 134/41Eliz/East7 : William Paget v. Edward Rolleston, clerk, Gilbert Rolleston, Wm. Watson, John Sheppard, John Townsend, Thos. Caldwell: "Horninglow Outwoods," in Rolleston, parcel of the manor of Burton-on-Trent, the manor and town of Rolleston (Stafford), parcel of the duchy of Lancaster, Seney Park, and the rectory and parish church of Rolleston.

[Beds]: views of account of the property of Harrold, Caldwell and Markyate priories. 31-32 Hen. VIII.

Copy of lease by the prior and convent of Caldwell to Anthony Darcey of the rectory of Tolshunte manor, Essex. 20 Hen VIII

I found only one reference to Caldwell, Yorkshire.

Sir Richard Hawkesworth, Knt., Wm. Staveley, Thos. Ingilby, John Barney, Fras. Carlile, Roger Palmer, Geo. Burnett, Edmd. Mawde, Richd. Smith, Wm. Batty, Wm. Caldwell. v. Michael Askwith, James Moore.: Manors of Ripon, Otley, Cawood, and Wistow, in possession of Toby Archbishop of York, in right of his archbishoprick. Privileges and jurisdiction within the liberties of said archbishopric. Whether the freeholders"in regard of suit and services within sd liberties shall be freed from their attendance at the assizes, quarter sessions, and gaol deliveries for the coy of York, and have hitherto been discharged from same by orders of the Cort of Exchequer"? &c., &c.: York. 22 Jas 1 1623-24

Release by William Grey of Merton, esquire, Thomas Irby, William Crosse, Thomas Knyghton of Thetford, and Thomas Lesse of Watton, who are enfeoffed, to the use of Henry Clerk, of a messuage and land in Asshill, to Humphrey Adam, John Adam, and Nicholas Markaunt, at the special request of the said Henry, of all their right in that portion of the said land with which the said Henry has enfeoffed the said Humphrey, John, and Nicholas, part lying on Brakysmeduefurlong, by land of the manor of Uphall, part abutting on Burywey, part at Genel mere by land [ called ] 'Collardes,' and abutting on land of the manors of Saham and Uphall, part in Caldwell felde by land of the manors of Panneworth and Uphall, part in the same field by lands of the rectors of Asshill and Houghton,and abutting on Caldewell medewe, and part at Calkepytte : [ Norf. ] 24 February, 5 Henry VII.