Of the familiy of Shardeloes of Amersham??? Definitely. The Alumni Oxonienses is definitive.
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No record found for his birth or baptism except that at matriculation to Oxford he was 17 years old.

Though Burke's Commoners states that he was born on 25 Jul 1727
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He is probably the Rev Thomas Drake, Ll B, D.D. who was rector of Amersham from 1754.  He married an Elizabeth, surname as yet unknown, from the baptism information for their daughter Charlotte Elizabeth at Amersham on 26 Sep 1764.

He is said to have had another daughter Isabella who m. Thomas Dorrien of Haresfoot, Berkhampstead.

The CCED shows that he was BCL, LLD and DD.  Further is documents that he was rector of Amersham from 24 Oct 1753 to his death (notice) on 30 Jun 1775.
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Michael Andrews-Reading in his Drakes of Shardeloes, p. 19, writes:

"In October 1753, William [Thomas' elder brother] appointed his younger brother Thomas Drake to the living of Amersham.  He served until his death in 1775, living in the spacious rectory on the hill behind the church and benefitting from the generous glebe-lands and tithes of the parish, which was generally accounted one of the richest in the country.  William next appointed his third son, John, as Rector in July 1775."
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The Alumni Oxoniensis has this entry for him in volume I of 1715-1886, p. 386:

Drake, Thomas, s. Montague Garrard, of London, arm. BRASENOSE COLL., 23 Feb 1744-5, aged 17; B.C.L. 1751, D.C.L. 1759, rector of Amersham 1753, and of St Luke's, Chelsea, died 12 April 1775.  See Alumni West., 325.
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The following baptisms are to be found in Amersham from 1753 to 1773 for children of Thomas Drake:

Last name First name(s) Year Of Birth Year Of Death  Year  Record set  Location    Bapt

Drake Mary Frances — — 1760   Buckinghamshire Baptism Index  Amersham, Bucks  28 Nov 1760
Drake Sarah — — 1762   Buckinghamshire Baptism Index  Amersham, Bucks  02 Jun 1762
Drake Charlotte Elizabeth — — 1764   Buckinghamshire Baptism Index  Amersham, Bucks  26 Sep 1764

So the fourth daughter mentioned in Burke is not found here.

The mother of all three baptisms is given as Elizabeth.
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These baptisms were found in the Wesminster register for Isabella, dau. of Rev [from the omages of the register] Thomas and Elizabeth Drake:

First name(s) Elizabeth
Last name Drake
Birth year 1756
Birth date 05 Feb 1756
Baptism year 1756
Baptism date 06 Mar 1756
Father's first name(s) Thomas
Mother's first name(s) Elizabeth
Parish St George, Hanover Square
County Middlesex
Country England
Page 109
Archive City of Westminster Archives Centre
Record set Westminster Baptisms

First name(s) Isabella
Last name Drake
Birth year 1758
Birth date 23 Apr 1758
Baptism year 1758
Baptism date 18 May 1758
Father's first name(s) Thomas
Mother's first name(s) Elizabeth
Parish St George, Hanover Square
County Middlesex
Country England
Page 154
Archive City of Westminster Archives Centre
Record set Westminster Baptisms
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His burial transcription:

First name(s) The Revd Dr Thomas
Last name Drake
Death year -
Burial year 1775
Burial date 21 Apr 1775
Place Amersham
Denomination Anglican
Occupation Rector
County Buckinghamshire
Country England
Document type Parish registers
Register type Baptisms, marriages & burials
Register year range 1726-1812
Archive reference PR4/1/4Q
Archive Centre for Buckinghamshire Studies
Record set Buckinghamshire Burial Index
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His will index on the national Archives:

Reference: PROB 11/1007/393
Description: Will of Reverend, Doctor Thomas Drake, Doctor of Laws, Clerk of Agmondesham , Buckinghamshire
Date: 30 May 1775
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In his commendably short will he left everyting apart from £50 for the poor of Amersham to his children and wished to be buried beside his wife in the vestry of Amersham parish church.  In other words his wife had predeceased him and is buried in Amersham.
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In the Upper Vestry of St Mary's church, Amersham is:

In Memory of/ the Rev. Thomas Drake Rector of Amersham,/ who died April 12th 1775/ And of his Wife Elizabeth/ Daughter of Isaac Whittington Esqr./ of Orford House in the County of Essex,/ who died July 17th 1765./ Faelices Animae! sit Honestum, et Amabile siquid/ Nulla Dies unquam memori Vos eximet aevo/ Moerens Frater p.c. [wall-tablet; Elizabeth Drake buried 26.7.1765; Rev’d Dr. Thomas Drake buried 21.4.1775 - Par. Reg.]

As transcribed by Michael Andrews-Reading in 1998-2007
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This looks strongly like their marriage, with his residence of Agmondesham:

First name(s) Thomas
Last name Drake
Residence Agmondesham
Marriage year 1755
Parish St George, Hanover Square
Spouse's first name(s) Elizabeth
Spouse's last name Whittington
Spouse residence Saint George Hanover Square
County Middlesex
Country England
Archive City of Westminster Archives Centre
Record set Westminster Marriages

And the image of the marriage register adds the clincher that he was "The Reverend" and give the full date of 31 March 1755.
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The transcript of the Marriage Licence is:

First name(s) THOMAS
Last name DRAKE
Licence year 1755
Licence date 25 Mar 1755
New calender date 25 Mar 1755
Bride's first name(s) Elizabeth
Bride's last name WHITTINGTON
Groom's first name(s) Thomas
Groom's last name DRAKE
Place Dioceses of England & Wales
Record set Faculty Office Marriage Licences

A copy of the original can be obtained for a trifling £15 from the Soc of Genealogists.
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