Was King Alfred the Great, King of the Wessex or King of England?

According to the Penguin Encyclopedia (2004), Alfred was king of Wessex, but not of England. The encyclopedia also says that "...He forged close ties with other English peoples not under Danish rule, and provided his successors with the means to reconquer the Danelaw and secure the unity of England." Danelaw: that part of England where Danish conquest and colonization
in the late 9th century left an imprint...on place-names, language and culture. ...in the 12th century all Eastern England from the Thames to the Tees was so designated." From this, we can safely deduce that Alfred was king of Wessex, but not of England.

He was the King of Wessex, England at that time, had not been unified.

Alfred was King of Wessex and King of England or the Englsih. Alfred was also known as King of the Anglo Saxons. https://en.wikipedia.org/wiki/Alfred_the_Great

Alfred successfully defended his kingdom against the Viking attempt at conquest, and by the time of his death had become the dominant ruler in England. He is one of only two English monarchs to be given the epithet "the Great", the other being the Scandinavian Cnut the Great.

England was not a unified country. Battles were being fought all over the English territories, Alfred fought against the Vikings for control of the lands.

Alfred the Great (849 AD - 899 AD)
King of the southern Anglo-Saxon kingdom of Wessex and one of the outstanding figures of English history, as much for his social and educational reforms as for his military successes against the Danes. He is the only English monarch known as 'the Great'.
Alfred was born at Wantage in Oxfordshire in 849, fourth or fifth son of Aethelwulf, king of the West Saxons. Following the wishes of their father, the sons succeeded to the kingship in turn. At a time when the country was under threat from Danish raids, this was aimed at preventing a child inheriting the throne with the related weaknesses in leadership. In 870 AD the Danes attacked the only remaining independent Anglo-Saxon kingdom, Wessex, whose forces were commanded by Alfred's older brother, King Aethelred, and Alfred himself.
In 871 AD, Alfred defeated the Danes at the Battle of Ashdown in Berkshire. The following year, he succeeded his brother as king. Despite his success at Ashdown, the Danes continued to devastate Wessex and Alfred was forced to withdraw to the Somerset marshes, where he continued guerrilla warfare against his enemies. In 878 AD, he again defeated the Danes in the Battle of Edington. They made peace and Guthrum, their king, was baptised with Alfred as his sponsor. In 886 AD, Alfred negotiated a treaty with the Danes. England was divided, with the north and the east (between the Rivers Thames and Tees) declared to be Danish territory - later known as the 'Danelaw'. Alfred therefore gained control of areas of West Mercia and Kent which had been beyond the boundaries of Wessex.
Alfred built up the defences of his kingdom to ensure that it was not threatened by the Danes again. He reorganised his army and built a series of well-defended settlements across southern England. He also established a navy for use against the Danish raiders who continued to harass the coast.
As an administrator Alfred advocated justice and order and established a code of laws and a reformed coinage. He had a strong belief in the importance of education and learnt Latin in his late thirties. He then arranged, and himself took part in, the translation of books from Latin to Anglo-Saxon.
By the 890s, Alfred's charters and coinage were referring to him as 'king of the English'. He died in October 899 AD and was buried at his capital city of Winchester.