TEFL accreditation, explained
There is no single worldwide TEFL authority. Words like "accredited", "regulated" and "recognised" mean different things depending on who is doing the accrediting.
Regulated qualification (government register)
In England, Ofqual regulates qualifications offered by approved awarding organisations. A regulated qualification has a qualification number (format like 610/1558/1), a level on the Regulated Qualifications Framework and a status such as "Available to learners" or "No longer awarded". You can look it up on Ofqual's public register.
Awarding organisation vs. course provider
Often the company selling the course is not the body awarding the qualification. For example, a provider may be an approved centre of an awarding organisation, and the register entry names that awarding organisation.
Accreditation bodies
Many providers also cite private or sector accreditation bodies. These are not the same as a government register. To judge one, check whether the accrediting body itself is recognised - in the US, by the Department of Education or CHEA (links on the verify page).
Levels and hours
Register entries list guided learning hours and total qualification time. Marketing "hours" (e.g. 120-hour) may count differently, so compare like with like.