When people outside the British isles (esp. Americans) say "British accent", they almost invariably mean (British) English, and usually the "received pronunciation" accent that British media generally uses.
They do not mean Irish or Scottish accents; if they did, they would have said exactly that, because those accents are quite different from standard (British) English accents. So different, in fact, that even Americans can readily tell the difference, when they frequently have some trouble telling English and Australian accents apart.
Also, to most English speakers, "English accent" doesn't make much sense, because "English" is the language. It sounds like saying a German speaker, speaking German, has a "German accent". Saying "British accent" differentiates the language (English, spoken by people worldwide) from the accent (which refers to one part of one country that uses that language).
They do not mean Irish or Scottish accents; if they did, they would have said exactly that, because those accents are quite different from standard (British) English accents. So different, in fact, that even Americans can readily tell the difference, when they frequently have some trouble telling English and Australian accents apart.
Also, to most English speakers, "English accent" doesn't make much sense, because "English" is the language. It sounds like saying a German speaker, speaking German, has a "German accent". Saying "British accent" differentiates the language (English, spoken by people worldwide) from the accent (which refers to one part of one country that uses that language).