Martin P-L writes:

Sister of Sir Horace Mann, bart, ext KB, ambassador at Florence [see below].

TFPL, 2017: This baronetcy expired with the death of the 2nd bart in 1814.  Burke’s “Extinct Baronets” (not wholly reliable, vide their article on the Barrington baronets) has Eleanor as the 4th daughter and, indeed, her only brother was the second baronet. The baronetcy had been created for her uncle, her father’s brother Horatio, with the remainder to the family of her brother but he had had only daughters.  Anyhow this superb information has led me to changing her name from Mary to Eleanor.

PS: The Ambassador at Florence is said by Burke to have been Horatio, Eleanor’s uncle, not her brother.
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Later I have found images, thanks FindMyPast, Family Search and Ancestry with the last being the best quality, of the baptism register page, transcript by me:

>                     St Martin-in-the-Fields  > 1740-1751

“    Baptized in September 1747            Born   159
“. . . .
“Eleanor Mann of Galfridus & Sarah        Aug:29
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Her baptism transcript from FindMyPast:

First name(s)           Eleanor
Last name               Mann
Birth year              1747
Birth date              29 Aug 1747
Baptism year            1747
Baptism date            23 Sep 1747
Father's first name(s)  Galfridus
Mother's first name(s)  Sarah  
Parish                  St Martin-In-The-Fields
County                  Middlesex
Country                 England
Archive                 City of Westminster Archives Centre
Record set              Westminster Baptisms
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Her burial register image, thanks Ancestry, transcript by me:

>            Lilford > Parish Registers  >  1813-1912

“BURIALS in the parish of Lilford cum Wigsthorp
“  in the County of Northampton in the Year 1822
“. . . .
“1823
“. . . .
“[Note in the Margin:]  N.B.*  Relict of Thomas first Baron Lilford
“Name:                  *Eleanor Lilford
“No:                    47
“Abode:                 Clifton
“When buried:           Febry. 21
“Age:                   75
“Celebrant:             L Powys, Rector of Titchmarsh
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Her burial:

First name(s)       ELEANOR
Last name           LILFORD
Birth year          1748
Death year          1823
Age                 75
Burial year         1823
Burial day          21
Burial month        Feb
Residence           Clifton
Parish              LILFORD
County              Northamptonshire
Country             England
Register reference  B0369/0027
Record set Northamptonshire Burials
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She wrote a will on 4 June 1803, added a first codicil on 4 Dec 1821 and a second codicil on March 12th 1822.

At probate her two daughter swore that their mother was Eleanoer Dowager Lady Lilford was late of Clifton Gloucester.

Additionally after her death the GWR wills department referred to her as of Clifton, Gloucestershire.

So I conclude that Clifton, Glos is where she died.

The will was about her many children.
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Their marriage transcription by FindMyPast:

First name(s)           Eleanor
Last name               Mann
Residence               Cottesmore
Marriage year           1772
Marriage date           31 Mar 1772
Spouse's first name(s)  Thomas
Spouse's last name      Powys
Spouse's residence      Lilford, Northampton
Denomination            Anglican
Place                   Cottesmore
County                  Rutland
Country                 England
Archive                 Record Office for Leicestershire, Leicester & Rutland
Archive reference       DE1920/4
Record set              Rutland Marriages
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