Wessex was one of the early Anglo-Saxon kingdoms, the only one to survive the Viking invasions of the ninth century. Under the rule of King Alfred the Great and his son and grandsons, Wessex assumed the leadership of the English-speaking peoples, first absorbing the rump of Mercia which the Vikings had failed to conquer in the early tenth century, then moving on to conquer the Danelaw territories by the middle of that century.
Traditionally, historians date the transformation of the kingdom of Wessex into the kingdom of England to 927, when King Alfred's grandson, Aethelstan, conquered Northumbria. Though this proved ephemeral, by 954 the conquest of the Danelaw was complete. Thereafter, there was only one English kingdom on English soil, and the West Saxon royal dynasty had become the first royal dynasty of a united English kingdom.
For more detail, see Stephen R. Bassett, The origins of the English kingdoms (1990); and Barbara Yorke, Wessex in the early middle ages (1996).