I cannot speak for England, but here in the US I have not seen many schools for teaching specifically English. This is because we learn English all throughout our regular schooling. However, there are many foreign language tutors which I would say is the most common.

Language schools

In the United States, such schools are usually called, simply, "language schools," but the schools choose their own terminology. As a generic term I would call them "language schools." For English, specifically, for speakers of other languages, the (confusing) terms are ESL (English as a second language), EFL (English as a foreign language), and ESOL (English for speakers of other languages) and I would probably say "ESL school." We do not usually use "academy" as an ordinary generic name. Schools may call themselves "academies" because it sounds impressive. Here are some real names of real schools: Berlitz Language Center The Boston Language Institute English Language Center - ELC Boston LAL Boston Boston International Academy Language Connections Boston School of English RoLa Languages AES World Languages and Cultures Institute Boston Academy of English

In the US, there are sometimes English schools in areas where there is a concentration of immigrants, but the names are usually in the native language instead of being advertised as an "English Academy". There are also language schools, like Berlitz, where people pay for classes to learn different languages, including English. That said, most people learning English in the US take English as a Second Language (ESL) courses which offered through the schools, local community colleges, or sometimes churches and civic groups. I have the impression that it's probably like this all over the Anglophone world.