There have been two Baronetcies created for members of the Barkham family, both in the Baronetage of England. Both creations are extinct.

The Barkham Baronetcy, of South Acre in the County of Norfolk, was created in the Baronetage of England on 26 June 1623 for Edward Barkham, later Member of Parliament

Member of Parliament

A Member of Parliament is a representative of the voters to a :parliament. In many countries with bicameral parliaments, the term applies specifically to members of the lower house, as upper houses often have a different title, such as senate, and thus also have different titles for its members,...

 for Boston

Boston (UK Parliament constituency)

Boston was a parliamentary borough in Lincolnshire, which elected two Members of Parliament to the House of Commons from 1547 until 1885, and then one member from 1885 until 1918, when the constituency was abolished.-History:...

. He was the son of Sir Edward Barkham (d. 1634), Lord Mayor of London

Lord Mayor of London

The Right Honourable Lord Mayor of London is the legal title for the Mayor of the City of London Corporation. The Lord Mayor of London is to be distinguished from the Mayor of London; the former is an officer only of the City of London, while the Mayor of London is the Mayor of Greater London and...

 from 1621 to 1622. Barkham was succeeded by his elder son Edward, the second Baronet. He was Sheriff of Norfolk between 1667 and 1668. He died without male issue and was succeeded by his younger brother, William, the third Baronet. He had no surviving male issue and on his death in 1695 the baronetcy became extinct.

The Barkham Baronetcy, of Wainflete in the County of Lincoln, was created in the Baronetage of England on 21 July 1661 for Edward Barkham. He was the son of Sir Robert Barkham, younger brother of the first Baronet of South Acre. The title became extinct on the death of Barkham's grandson, the third Baronet, in 1711.

Barkham Baronets, of South Acre (1623)

• Sir Edward Barkham, 1st Baronet
  Sir Edward Barkham, 1st Baronet, of South Acre
  Sir Edward Barkham, 1st Baronet of South Acre was an English politician who sat in the House of Commons in 1625 and 1626.Barkham was the son of Sir Edward Barkham. He matriculated from King's College, Cambridge in spring 1611 and was awarded BA in 1613 on the visit of Prince Charles. He was...
  
   (c. 1595 - 2 August 1667)
• Sir Edward Barkham, 2nd Baronet (1628-1688)
• Sir William Barkham, 3rd Baronet (28 February 1639-28 December 1695)

Barkham Baronets, of Wainflete (1661)

• Sir Edward Barkham, 1st Baronet (20 March 1631–14 September 1669). Barkham was the son of Sir Robert Barkham, younger son of Sir Edward Barkham, Lord Mayor of London
  Lord Mayor of London
  The Right Honourable Lord Mayor of London is the legal title for the Mayor of the City of London Corporation. The Lord Mayor of London is to be distinguished from the Mayor of London; the former is an officer only of the City of London, while the Mayor of London is the Mayor of Greater London and...
  
   between 1621 and 1622. His mother was Mary, daughter of Richard Wilcox. In 1661 he was created a Baronet, of Wainflete in the County of Lincoln. Between 1664 and 1665 he served as Sheriff of Lincolnshire
  Lincolnshire
  Lincolnshire is a county in the east of England. It borders Norfolk to the south east, Cambridgeshire to the south, Rutland to the south west, Leicestershire and Nottinghamshire to the west, South Yorkshire to the north west, and the East Riding of Yorkshire to the north. It also borders...
  
  . Barkham married Anne, daughter of Sir Robert Lee, in 1656. He died in September 1669, aged 38, and was succeeded in the baronetcy by his son, Robert.
• Sir Robert Barkham, 2nd Baronet (d. c. 1701)
• Sir Edward Barkham, 3rd Baronet (c. 1680–13 September 1711)