I prefer British accents but I'm American so that could be why. 

My favorite accent is the Scottish accent!

Alexander you are of course correct about there being no 'British accent.' As you alluded to, someone from Glasgow doesn't sound much like someone from London, and yet they are both British accents with both cities being within the geographical confines of Great Britain. And that's not even mentioning the variation in accent within the different countries.

The idea of a 'British accent' is a misnomer, but for whatever reason people from outside the UK tend not to distinguish England from Britain. But you can take it as read that when most people say British accent they actually mean 'English' accent. And the English accent they are thinking of is the accent from the South East of England i.e. the one that is most commonly heard in the media, and the one that the English language dictionaries use as the basis for British pronunciation.

From the perspective of someone from the UK it is completely intuitive that there isn't a British accent, because we know about the different countries and the fact that there is a lot of variation between regions, but to non-Brits this isn't so intuitive.

Much more convenient to just say British, rather than specify exactly which kind you mean. It used to bother me too, but to be honest pointing this out all the time just seems a bit pedantic, not least because the idea of what is England vs Great Britain vs the UK can be a bit complicated. For example I could be pedantic about what you wrote and say that Great Britain refers only to the land mass of England, Scotland and Wales and is therefore only composed of three countries. It is the United Kingdom (of Great Britain and Northern Ireland) that is comprised of four countries. 

There is no "British" accent. Britain is made up of 4 countries ( England, Northern Ireland, Scotland, and Wales,) that all have completely different sounding accents, and within those countries accents vary differently. So you can’t really say British accent.

I prefer British cause I understand it better than american ,but I have to learn american because it's using more in jobs