There are currently around 5,000 Turveys in the world, as follows:
The population in England is concentrated around Bedfordshire and Worcestershire. This has been the consistent pattern in all censuses since 1841, except that there has been a general urbanisation and diffusion of the population. Census returns showed a steady growth in Turvey population:
The following map shows the distribution of Turveys in 1841 according to the census:
The blue lines shows the migration patterns that can be seen on this map:
At least three Turvey lines have been tested for their Y-DNA - the male sex chromosome which is always passed down from father to son. These have revealed:
Generally speaking, since the establishment of surnames in England in the 1300s, these have also passed from father to son and therefore should match the inheritance of Y-DNA. However, there are a number of key mechanisms that can happen to interrupt this transmission, which would result in men sharing the Turvey surname having different Y-DNA. In particular:
Therefore, there is a high chance that there would be some interruption in the 15 generations between 1300 and 1750.
Earliest recorded Turveys
The earliest recorded Turveys include:
Around a third of all Turveys today are descended from Turveys in Worcestershire, including the descendents of William Turvey (1). However, there is no mention of an Turveys in the subsidy rolls for Worcestershire in 1332  or 1327  nor in the neighbouring counties of Gloucestershire & Bristol  
The earliest mention of a Turvey in the county is of yeoman George Turvey of Walcot, who was imprisoned in Worcester Gaol in 1510 on account of a debt of £17 he and two others from Pershore owed a London merchant. It was recorded that George Turby [sic] was in possession of 3 messuages, 100 acres of land, 20 acres of meadow, 100 acres of pasture, 10 acres of wood, and 100 acres of moor and heath in Walcot, worth 5marks (£3-6s-8d) a year. Walcot is located in the parish of Pershore, 9 miles southeast of Worcester. His will was recorded in 1557 as "George Turv, yeoman, Walkott Worcester".  Walcot is recorded in the hands of John le Blake in 1313, who held it from the Abbey of Pershore and the Abbey of Pershore also held it in 1346  and 1428.
A Richard Turvey was recorded in the Lay Subsidy of 1524 in Pershore assessed at £3-10s.
The high proportion of Turvey descendents from Worcestershire may be due to a possible "founder effect", where an ancestor moved to the area sometime in the 1400s and was particularly successful, leading to a larger than normal number of descendants. It is possible that this person could have been a retained soldier who fought in the Wars of the Roses and was rewarded with land in Worcestershire.
A David Turvys was listed as a goldsmith and Burgess in nearby Bristol in 1528.  Another will, Rycharde Turvey of Drake Broughton, was recorded in 1542. Drake Broughton is 1 mile west of Walcot, in the north end of Pershore Holy Cross parish.
Pershore parish registers begin in 1540. Early records include:
Ann Turvey, wife of Bartholemew Turvey, was buried 10 Feb 1615 in Pershore
The next records are from Droitwich, 7 miles north of Worcester:
Around the same time, there are two records from Pinvin, a chapelry of Pershore parish, 2 miles north of Pershore:
Meanwhile, a Rychard Turvey married Joanne Walker on 22 Jul 1599 in Offenham, 7 miles east of Pershore. 
A graduate of Oxford University, Richard Turvey (b 1602), is listed receiving a B.A. on 6 Dec 1622 and an M.A. on 22 Jun 1625. He was appointed Rector of Sedgeberrow, Worcestershire, on 9 Nov 1627, on the death of the previous incumbent. Papers dated 28 Sep 1648 indicate that he was charged by the victorious parliamentarians following the end of the English Civil War. 
The Heraldry of Worcestershire talks of the Turveys of Walcot, "a family possessed of considerable landed property". Edward Turvey of Walcot, esq, was fined in 1625 for "not taking knighthood on the coronation of Charles I".
In the far north of the county, the parish records of Dudley record a family of Turveys:
The Hearth Tax records for Worcestershire in 1664 listed nine Turvey households who were liable for the tax:
The Thomas Turvey, esquire, listed in walcot, is presumably the same person as that listed as High Sheriff of Worcestershire in 1666 . He may also be the Thomas Turvey, gentleman, who was involved in six court cases listed in the "Worcestershire Fines" in between 1649 and 1654.
Richard Turvey of Walcot died in 1658, aged 60, leaving his daughter Elizabeth as heir, and his property passed to their children, the Earls of Plymouth. . He may have been the Richard Turvey, gentleman, who was involved in two court cases in 1656 & 1657 
Thomas Turvey bought the Manor of Breedon, 7 miles south of Pershore, in 1667.  A "Thomas Turvey of Bredon" was included in Blome's "list of the gentry of Worcestershire" in 1673. A Thomas Turvey, "armigerum" (knight), is listed in six court case between 1663 and 1675, including in Breedon and Wadborough.  A John Turvey of Bredon was listed as High Sheriff of Worcestershire in 1668. .
East Anglians Turveys
The 1841 census listed a total of ten Turveys in Suffolk and 17 in Norfolk, located in eight parishes spread throughout the counties. Although this is just 5% of the total number of Turveys in England at the time, and just 1 in 25,000 of the population of the two counties , the family had been present in the area for many centuries.
The first recorded Turvey in East Anglia was John de Turvey of Huntingdonshire, listed in 1328 as a surety. Clearly a man of some means, he lived less than 30 miles northeast of the village of Turvey. Seventy years later a Turvey is included in the list of the rectors of Alderford, a village ten miles northwest of Norwich. This church had it's patron as the Dean of Norwich and there is no record of the same person elsewhere, so it is unclear whether he left any mark on the county..
The Subsidy of 1524 recorded two Turveys in Suffolk with property of more than £1 in goods or annual income (roughly equivalent to £20,000 in 2016 ). This was out of a total list of 17,000 taxpayers recorded, indicating that the family has declined somewhat in the following three hundred years. The two recorded were John Turvy, in Becclys [Beccles], with £4 in goods and Robert Turvey in neighbouring Wyrlyngham [Worlingham] with £1 in annual wages. The Subsidy of 1568 had a higher threshold of £3 in goods, covering only 7,700 taxpayers; no Turveys were recorded in that return. 
The earliest parish registers date back to 1538 when the protestant king Henry VIII ordered for religious reasons that every wedding, baptism and burial should be recorded. Parish registers, however, have patchy coverage and not very many are available online. The earliest recorded on FreeREG in the birth in 1561 of Johes Turvy in Foulden, Norfolk  followed by the marriage in 1570 of George & Agnes Turvye in Rushall. They baptised a daughter the following year in neighbouring Dickleburgh and another Turvey was baptised the year after in next door Scole. Three Turvey marriages were recorded in the 1590s in the town of Dunwich.
The registers of Wortham, near the Norfolk/Suffolk border, record a series of Turveys from the late 1600s. In 1697 they record the marriage of Thomas Turvye [sic] and Maria Cutting, and the death two years later of Robert Turvye, "old man" - possibly Thomas' father. There were at least three Turvey families recorded in the early 1700s in the Wortham registers and many of the Turveys listed in the census in Suffolk and Norfolk can be traced back to this parish.
The earliest record of a Turvey in the United States was John Turvey, from Ashford, Kent, England who sailed to Massachusetts in 1634 on the ship Hercules. He was listed as a servant of Dr. Comfort Starr, a surgeon who settled in Boston and became one of the earliest benefactors of Harvard University.
However, the ancestors of most Turveys in the United States migrated there from Britain in the latter half of the nineteenth century. Between 1820 and 1957, 107 Turveys were listed on passenger lists travelling from Britain to New York and Boston.  Census returns showed only 1 Turvey family in 1840 - perhaps the family of Hyatt Turvey - which had increased to 147 families by 1880. Two thirds lived in Ohio and the population was limited to 12 states. By 1920 the total number had reduced to 107 families but the population was now spread through 27 States; the number of families living in Ohio had halved.  Only sixty four people were listed in 1920 with a British birthplace. 
Four Turvey brothers from Essex, England - James, George, Frederick and Thomas, were transported to Australia in the 1830s, becoming the first Turveys in Australia.  The population grew steadily in the twentieth century. Electoral rolls in Victoria listed 30 Turveys in 1903, growing to 85 by 1936. By then there were 248 listed throughout Australia as follows:
Turvey Park, a suburb of the city of Wagga Wagga in New South Wales derives its name from Thomas Turvey, the transported convict who later became the licensee of the Bridge Hotel.
Twenty seven Turveys were listed in the 1891 Canadian census as having a British birthplace - of whom 21 were in Ontario.  Today there are nearly 400 Turveys in Canada, mostly in Ontario and British Columbia. 
Included in the 4,000 English settlers who moved to South Africa in 1820, was Edward Turvey, born in Dublin, and his family. 
There are a handful of records of Turveys living in Ireland. In 1771, a Thomas Turvy was recorded marrying Ann Barber in a Catholic church in Dublin. In 1802 and 1803, two sisters, Lidiam Perdue and Matildam Perdue were recorded being baptised in the same church with godparents of Martha and Matilda Turvy respectively. 
In 1781, Edward Ford Turvey, the ancestor of the South African Turveys above, was born in Dublin apparantly to an Anglican family. His father, John Turvey, was born in 1738. Edward lost most of his fortune in a business venture with two ship owners, Aiken and McGrath. On 4 February 1805 he married Julia Wright nee Daniel, a rich widow. Their first three children, Mary, Eliza Juliana and Edward Mortimer, were born in Dublin in 1806, 1809 and 1811 respectively. In 1820 he organised a party of settlers to move to South Africa. 
In 1873, the weddding was reported in St Werbergh's, Dublin of Alexander Turvey, who lived in Longford and was a Corporal in the 8th Hussars, a predominantly protestant army regiment. His father was listed as Arthur Turvey, a civil engineer. 
Barons of Turvey
A separate, unrelated, family, is the Barnewalls. As early as 1534 Sir Patrick Barnewall was styled "of Turvey". His son, Sir Christopher Barnewall built Turvey House in Dublin in 1565, which gives its name to the adjacent district. His grandson, Sir Nicholas Barnewall was made Baron Turvey in recognition of his service during the English Civil War. 
 1,964 people listed in 1998: http://www.nationaltrustnames.org.uk/Comparisons.aspx?name=TURVEY&year=1998&altyear=1881&country=GB&type=name
 The Turvey Name in History, The Generations Network, 2008