Whilst the county of Yorkshire seems to have been the main location for the Tennant family
in England the oldest english record found so far is just over the current border into Lancashire.

Thomas Tennant chris 7 Apr 1549, Middleton by Oldham, Lancashire.
Source:  Morman familysearch.org
Relevance: Earliest found England, record says baptised,not born,difference relevant below.

Thomas Tennand  married 16 Nov 1560, sp Agnes Hagger,  Methley, Yorkshire
Source:  Morman familysearch.org
Relevance: Earliest found in Yorkshire. Note, if previous Thomas(1549) was christened at birth 
then not same person but if baptised several years later then this could be his marriage.
The geographical locations are quite close, though different counties.

James Tennant (b1600c) lived in Nealying, Yorkshire. F= John Tennant, Yorkshire.
Brother = Marmaduke Tennant, mother was Alice Fawcett daughter of Marmaduke Fawcett.
Source:- Ancestry.com ref  Kimball G.Everingham says James married after 1625
Relevance: Start of Marmaduke as a christian name in one branch, still found in 1877.

Marmaduke Tennant (b1600c) Yorkshire. (see brother James 1600)
Source:book The Cromwellian Settlement of Ireland by John P. Prendergast
Relevance: Marmaduke Tennant  subscribed for land in Ireland between 1642 and 1675

Marmaduke Tennant  chris 24 Aug 1600, Walton in Ainsty,Yorkshire  f=Thomas Tennant
Sp=Eunis Bennett, m 11 Feb 1636, London.
Source: Mormon familysearch.org ref International Genealogical Index - British Isles.
Relevance: This Marmaduke has different parents than the one above, otherwise same person? Checked
father's name on Mormon site - no help. Mormon info unreliable unless cross supported.

Richard Tennant, estimated b1645c, m 4 Jul 1665 in Tathem Lancashire,sp Margret Dowbiggin 
Sons= Oliver b 1668 and Thomas b:1680
Source: Ancestry.com search on Richard gave Diane E.Speake info from Wed.Reg. Tatham.
Relevance:- Thomas, too old to be Thomas/Judith but could be his father.  Richard = key family
name plus son called Thomas. Using name Oliver = Cromwellian sympathy?

Richard Tennant b1670/1680c m. Anne Raper, earlier members of Raper family,lived nr Thirsk, Yorkshire.
Children=William b1695/1700c, Elizabeth b1700/1710c, Stanhope b1705/1710c

Thomas Tennant, chris 17 June 1701, Walsall, Stafford England. F=Richard, M=Susannah
Source, Mormon IGI,
Relevance:- Only Thomas in search(1699-1739) of England that has Father called Richard.
If born 1701 when christened, then would be 48 when son Richard born to Thomas/Judith in Ireland.
Several other Thomas's also in this search period, some without fathers name. 

Thomas Tennant b/chris 1719, York, F=Joseph, M= Thomasin. Bro= James b1721
Source, Mormon:- familysearch.org
Relevance:- Could be Thomas of Thomas/Judith fame but is Yorkshire branch ie not west coast of UK.

Thomas Tennant, (1763-1833), m. Elizabeth Mason.
Woolen merchant, Yorkshire, 3x Mayor of Leeds
Source: Sarah Mills on //genforum.genealogy.com/tennant/messages/744.html

Thomas Tennant, Born 13 June 1779, f= Christopher, m= Isabella. 
sp= Elizabeth Thompson, m in 1804, lived in Wesleydale, Yorkshire.
Children include Thomas, William, James.
Source Ancestry.com search on Thomas gave Thistlethwaite-Ahrens info.
Relevance:- None except called Thomas

Thomas Pierce Tennant, m  in Yorkshire in 1871 to Eliza Roadhouse plus probable son Thomas Pierce
born & died in Tynemouth 1893.
Source Ancestry.com search on Thomas Pierce gave Civil Reg Index for Barnsley
Relevance:- Only use of Pierce as second name found, other than in my branch. The Yorkshire
branch in general goes back earlier than the Irish branch so this man perhaps went from Ireland
to Yorkshire in more recent times.
Please contact me via email at the foot of this page if you have info on this Thomas Pierce.