The Heptarchy

These are the kingdoms the Saxons fram'd,
And from their number the Heptarchy nam'd,
Kent, East Anglia, Sussex, Wessex,
Northumberland, Mercia, Essex.
When the natives, who long for their country had striven,
At last to the mountains of Wales were driven,
By Jutes and Angles from Germany's shore, &c.
- "The Heptarchy," J.G. Cuckow: Our Native England; Being the History of England Made Easy
(J. and C. Mozley, Paternoster Row, London, 1868)

Long before George R.R. Martin wrote A Song of Ice and Fire and HBO aired Game of Thrones, the Seven Kingdoms were those of England, not Westeros, and they have been called the Heptarchy (Greek for "Seven Realms") by historians since Henry of Huntingdon wrote Historia Anglorum (History of the English) in the 12th century.  The Heptarchy began around AD 500, after the Roman Empire withdrew from Britain and Germanic peoples such as the Angles, Saxons, and Jutes moved in.  It began to transition to the unified Kingdom of England after Egbert of Wessex briefly took over Mercia and Northumbria around 830, and was effectively ended when Æthelstan was crowned King of the English in 925. 

The Kingdom of England lasted until 1707, when it combined with the Kingdom of Scotland to form the Kingdom of Great Britain, which merged with Ireland in 1801 to form the United Kingdom (UK).  Modern historians consider the term inaccurate, as it ignores the many minor kingdoms, fiefdoms, and other powers present in Anglo-Saxon England.  This map in J.G. Cuckow's book shows the Heptarchy, though Scotland and Wales are not shown in detail, and the capital cities are omitted.  Here, then, are the known capitals, going in alphabetical order by kingdom.

East Anglia:  Rendlesham, later Dummoc
Essex:  London (now the capital of England, Britain, and the UK)
Kent: Unknown, though one must have existed
Mercia: Tamworth
Northumbria:  Bamburgh (northern kingdom of Bernicia), York (southern kingdom of Deira)
Sussex:  Chichester
Wessex:  Winchester