The rest of the entry for "English" says:
The term was used from earliest times without distinction for all the Germanic invaders -- Angles, Saxon, Jutes (Bede's gens Anglorum) -- and applied to their group of related languages by Alfred the Great. After 1066, of the population of England (as distinguished from Normans and French), a distinction which lasted only about a generation. In pronunciation, "En-" has become "In-," but the older spelling has remained. Meaning "English language or literature as a subject at school" is from 1889. Old English is from early 13c.
Alfred the Great ruled from 871 to 899, so the term English to refer to language can be roughly dated to this era. Although English surely existed as a set of dialects or a language by this point (as Old English dates from around the 5th century), it is unclear at what specific point "English" became the language name. However, there is some reference here which says that speakers of Old English called themselves "Englisc"--which may mean that the word for the group of people dates back way before Alfred named their language (which makes sense--why would you necessarily name your own language).
The name England can apparently be found in its current form from the 1500s, with use dating back to 897:
The name "England" is derived from the Old English name Engla land, which means "land of the Angles". The Angles were one of the Germanic tribes that settled in Great Britain during the Early Middle Ages. The Angles came from the Angeln peninsula in the Bay of Kiel area of the Baltic Sea. According to the Oxford English Dictionary, the first known use of "England" to refer to the southern part of the island of Great Britain occurs in 897, and its modern spelling was first used in 1538
So, from these, there are two options. Either Englisc was first coined by the Angles and other invaders themselves, which would date the term before Alfred the Great (and possibly way back to the 5th century).
Or, both terms developed within years of each other. I would hazard a guess that Alfred the Great adapted the term English while he was king. This puts both terms in the period between 871 and 899. Since there is a set date for England's coining, which was toward the later part of Alfred's reign, it may be safe to say that English came first.
Either way, it seems as if English in some form predates England. However, there are no solid sources I could find for or against this.