Go back thirty years or more and elocution lessons were popularly taught in schools and through private classes to help native English speakers speak the language better. Elocution focused on training learners to speak with the clearest possible pronunciation. Often it was seen as a way to change speech toward a more upscale or powerful sounding tone. Either way, many prominent people have used elocution training to develop strong speaking voices. (Margaret Thatcher, Samuel L. Jackson, Cate Blanchett and Vanessa Redgrave to name a few).
According to SpeechSchool.TV (the leading speech training site on the internet) elocution students today are just as likely to come from other languages seeking accent training as they are native speakers wanting elocution lessons.
While elocution and accent training have different types of focus, the subject material taught is much the same. Elocution focuses on teaching clear, pronunciation in a neutral accent covering all sounds in the language. Accent training comes from the point of view that to learn clear spoken English, the learner must do so by adjusting their accent to the clearest and most neutral form of English. It is not easy for students to improve English accent.
The old art of elocution is thus being transformed to work with second language learners coming from a wide variety of different accents. The focus is not to remove a native accent completely but rather to give the speaker clear and neutral pronunciation that will put them in good stead to speak English well wherever they travel in the world.
SpeechSchool reports that about 70% of their students in their highly popular English Accent program come to English from another language. Their focus is on acquiring a Standard English accent to make their own speech clearer. However still 30% are native speakers and there focus is more on elocution, learning to speak the language more clearly or in some cases resolving a speech impediment such as mumbling or stuttering.
More information on the elocution and accent training program from SpeechSchool can be found on the accent training course page.