Since you don't mention teaching exclusively in English, the closest thing appears to be English for specific purposes or ESP. There are many subtypes, such as
- English for academic purposes (EAP), which can be further subdivided in
- English for academic science and technology,
- English for academic medical purposes,
- English for academic legal purposes,
- English for management, finance and business;
- English for occupational purposes:
- English for professional purposes (e.g. English for medical purposes, English for business purposes),
- English for vocational purposes.
The teaching method may be different from the method for "general English", but the main difference is in the types of materials and exercises that are used. For example, English for academic purposes will put more emphasis on how to write papers. The materials will depend on the subject people are studying, e.g. sciences, medicine, law etc., especially to learn the vocabulary needed in a specific discipline, but also grammar and register.
If the teaching is entirely in English, the approach is known as a direct method. A direct method requires teaching methods that are different from bilingual methods, especially at the lower levels, since the teacher can't rely on translations. However, the direct method as such is unrelated to the concept of teaching English for specific purposes.
In schools, e.g. the European Schools, it is also possible that certain subject are taught in English (as a foreign language). This is referred to as bilingual education. One type of bilingual education is known as two-way bilingual education. There has been research in this type of education, for example, at Wix School in Battersea, a primary school in the UK; see the article Research shows bilingual education works (Wandsworth Council, 19 March 2012):
One-way immersion is where a subject is taught in another language. Two-way immersion, which is the system used at Wix, involves students whose first language is English and those whose first language is French being enrolled in the same class.
Dr Meier said: "Bilingual education is based on the view that language is primarily a medium of communication and is best learnt by using it to convey meaning. My research in London and Berlin has found that students taught in two-way programmes form a more cohesive group, with greater conflict resolutions skills. Therefore, one-way and especially two-way immersion programmes could form part of a wider language acquisition and social cohesion strategy, and should be considered by schools and policy makers as a viable option."
(In the above example, the foreign language was obviously not English, but the principle is the same.)