Just found a Google ebook A genealogical and heraldic history of the extinct and dormant baronetcies of England, by John Burke, Esq and Sir John Bernard Burke, Esq which lists the Mawbey pedigree.
The Joseph husband of Charlotte mentioned above appears to have been the only son of the first Sir Joseph Mawbey (1) [1730-1798] and left no male heirs.
When Sir Joseph (2) died on 28 August1817, the baronetcy became extinct.
It had been created for his father on 30 July 1765.
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Sir Joseph Mawbey (1) had a older brother John, and their father was also a 'John Mawbey'.
Both boys married their cousins - John, Martha Pratt, and Joseph, Elizabeth Pratt.
Sir Joseph Mawbey (2) married Charlotte Caroline Henchman on 9 August 1796.
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According to Burke & Burke, Lady Elizabeth Mawbey died at Botleys Park estate on 19 August 1790 and was buried in the family vault in Chertsey chancel.
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So it seems that in order to track down the parents of my George Mawbey, I have to go back further in time.
The last John Mawbey was the only son of the youngest son, William, of Erasmus Mawbey.
William was the youngest of Erasmus's seven sons born to his first wife.
Erasmus then had five more sons to his second wife.
So maybe George Mawbey descended from one of the remaining 11 Mawbey men (not counting William).
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Alternatively, Erasmus's father Richard had a brother, Thomas, whose son William is described as the progenitor of the Mawbeys of South Kilworth in Leicestshire.

JOSEPH MAWBEY JNR BORN CHERTSEY, SURREY

In 1805 a birth of a Joseph Mawbey to Joseph Mawbey Snr and Charlotte took place in the town of Chertsey in Surrey.
Baby Joseph must have not been expected to live, because he was baptised on the same day.
Shortly afterwards, he died.
In 1810, the burial of a Charlotte Mawbey took place at Christ Church, Southwark.
The father of the deceased child and mother was the son of the original Sir Joseph Mawbey who also bore the title of 'Sir'.
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Chertsey is a very old English town on the banks of the River Thames.
It appears in the Domesday Book under a different spelling and was a Saxon stronghold.
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Sir Joseph Mawbey and his wife Eliza lived in the neighbouring parish of Botleys.
There is a memorial to Eliza in the Anglican church at Chertsey where she was buried in the family vault.
 

MORE ON ENGLISH MAWBEY PEDIGREE

I found another very helpful Google ebook, The baronetage of England, Vol 3, by Edward Kimber and Richard A Johnson, printed 1771, which lists all the members of the early English Mawbey family from whom Sir Joseph Mawbey was descended (pp.221-225).
It is written in the same precise manner of the first book of the Bible, Genesis.
A common thread is that many of the Mawbey men married twice, and one, thrice.
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Looking at the males of the 19th generation, the 12 sons of Erasmus Mawbey, only Richard, James and Isaac left male heirs.
Richard had a son Erasmus b. 1695 who had a son Erasmus.
James had a son James Jnr d. 1754 who fathered several children.
Isaac had twin sons, Abraham and Isaac, bap. 3 February 1694, who died, but then had another son, Isaac, who survived.
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Of the 21st generation, there was Francis, son of John Mawbey b.1693 to his first wife, J Shepherd.
Coincidentally, my father's baptismal name was Francis.
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Another of the sons of Erasmus Mawbey, Joseph, was killed in marine service at the seige of Gibraltar.

ANOTHER GEORGE MAWBEY

Another George Mawbey, not my GG grandfather b. 1809, was tried for theft of two brass cocks from his employer in London's Central Criminal Court on 5 February 1844.
Mawbey was gas fitter for the Chartered Gas Company in Horseferry-road, Southwark, and had taken the brass cocks when he went into the storeroom to get meters.
He was apprehended by the storeman and pulled the two brass cocks from his pocket before the police arrived.
In court, Mawbey apologised and said he did not know what induced him to take his employer's property.
He had worked for the company for nine years and was said to have been of unexceptional character and given every satisfaction.
Mawbey was found 'not guilty'.
[Source: http://www.oldbaileyonline.org Ref No. t18440205-627]