Origin of 英国 (England)
In the article 论国名与国号 it is mentioned that 英国 stems from 英格兰.

On Wikipedia they mention that it comes from 英吉利 (English) and 英格兰 (England):


  The written form of Yīngguó in Chinese is made up of two characters: 英国. The first 英 (yīng) as an adjective means "outstanding" and "fine", and as a noun means "flower"; the second is 国 (guó) which means "country", "state" or "kingdom". Originally the adjective word was written as 英吉利 Yīngjílì as an approximation of the adjective word English, and is still used to mean English in the Chinese word for the English Channel 英吉利海峡 Yīng jí lì hǎi xiá. The noun word was written as 英格兰 Ying ge lan for the noun England, also 苏格兰 Su ge lan for Scotland, 爱尔兰 Ai er lan for Ireland and 威尔士 Wei er shi for Wales. Also in history books Great Britain is written 大不列颠 da bu lie dian, from 大 (Great) and the sounds of the words 不列颠 similar to the sound interpretation.


I couldn't find any older (and better) references explaining the origin of 英.