I’m using the term British to refer to all of the UK, ie England, Wales and Scotland. I do this because I need a word for that, and because technically the big island is Britian. (The smaller one is Ireland).
Even something as simple as the identity of Andy Murray, the Wimbeldon tennis champion, is an interesting case. He is Scottish and identifies as Scottish. When he loses, English newspapers call him a grumpy Scot, when he wins he is declared British (which most non-British people equate with England).
The UK is made up of a number of different sub countries. All of which have a strong national identity and don’t like being called by another countries name. Refer to a Scot as English and you might get a punch in the nose. Heck in a little under 100 days, the Scottish will vote wether they will stay part of the UK.
I remember a line from Torchwood, where an American refers to one of the characters as English and she responds sternly, “Actually I’m Welch, not English.” There are whole TV channels where everything is in Welsh. So you have to be careful not to use the wrong word.
Then of course there is Ireland. Geographically Ireland is the “smaller” island in this group. (In this kind of thinking, I don’t think we want to use the term British Islands). Politically it is split with most of it being the independent Republic of Ireland, and a small portion of it in the north being part of the UK – whose name is technically “The United Kingdom and Northern Ireland”.
Still, these three countries have a lot in common and when you want to refer to them together, you need a term. I’m using British. Any UKians reading this please don’t take offence.