Learning/teaching English by phone has long been practised. It is particularly popular in France and became common in Paris towards the end of the last century, before the use of the Internet. It is very practical, not to mention eco-friendly, since neither student not teacher needs to leave their office, home or even bed. It also places a heavy emphasis on listening and pronunciation since non-verbal communication is excluded.
It can of course be for any learner, not just business execs, though beginners are not ideal for English by phone (yet need not necessarily be dismissed out of hand).
In one typical arrangement, lessons are 30 minutes long, and of course scheduled beforehand. The student calls the teacher at the given time. The lesson will typically revolve around discussion of a newspaper article or other text that has been faxed (emailed) to the student (or sent to the teacher by the student) based on his/her interests, possible homework from a previous lesson, perhaps grammar, vocabulary or pronunciation points that the teacher/student want(s) to focus on. Generally it is not necessary or fruitful to use a text book. Almost any item from the student's realm of work or interest could form the basis of a lesson.
30 minutes is probably long enough for any lesson by phone as far as the student is concerned. For the teacher, lessons by phone can be extremely tiring and demanding, especially if done in long stretches - many students one after the other. Having said that, experienced teachers find ways to adjust to the heavy demand it places on listening.
Today, with mobile and especially smart phones, many other possibilities arise such as the exchange of documents, photos, videos screen-to-screen.
English by phone has to en extent been supplanted by English by Skype (etc) yet the two are not quite the same and English by phone has an immediacy and focus on listening and speaking lacking in the usual type of English by Skype lesson.