In geography, a continent is a connected landmass, typically large enough to have more than one climate. There are Africa, Eurasia, America, Australia and Antarctica. In addition to continents, there are islands.
Another division of the world is in world parts (the English language fails to have a single word for this, which is the cause of this mix-up). Those are: Africa, Asia, Antarctica, Europe, North America, South America and Oceania.
World parts include islands. Therefore, Britain is a part of Europe, but not of Eurasia.