Ok, let's try and resolve this.
One of my history lectures remarked something along the lines off "Europe is not a continent, it's a penisula attatched to Asia" (Indeed, most of Europe and Asia is all part of the Eurasian plate) The vagueness of what Europe actually is, is highly problematic for the Russians, who are not quite European but not quite Asian at the same time. Geographically, Europe's considerd a continent, but its a rather vague construct of a continent. Being on the same geographic plate as the rest of Asia, and indeed, if you look at a world map, Europe is but a large sticking out bit from Asia.
But of course, Europe is very different to Asia- In climate, in lifestyle, people, history and culture.....and it is these things that make Europe what it is. Europe is a histrio-cultural construct which started with the Ancient Greek's and Hellanistic Civilisation, spread across "Europe" by the Roman Empire, which in turn spread Christanity. The collapse of the Roman Empire led to the rise of the Barbarians, whom evolved Europe into the Middle Ages. The Middle Ages ended with the rennaisance of the old Greco-Roman ideals of civilisation which set Europe on a course where it will come to dominate the world, with exploration and colonisation (the creation of "Neo-Europe's" in North America, Australia and New Zealand) and industralisation, this global dominance in part ending with the Total War's which would in turn lead to the modern world we know today.
Unless you think that Britain was not affected by such things as the Roman Empire, Christanity, the Rennaisance, the Enlightenment, colonialism and industralisation, then Britain defiantly is part of Europe.