There is currently NO independent, international board of accreditation or assessment for TEFL certificate providers. This means that each institute, school, or organization recognizes their own certificate and accreditation comes from good practice, professional standards and reputation.
There are a number of organizations which have been set up nationally. And there are a number of organizations which have been set up by schools as supposedly independent accreditation agencies to accredit their own courses. These latter fall under the banner of TEFL Scams.
The simple truth is that unfortunately, many TEFL courses which claim to be accredited are not and when taking a course, great care should be taken in checking out accreditation credentials which are often claimed but also often faked.
The following are commonly cited as accreditation agencies by course providers. Not all of them are reputable or trustworthy.
ACCREDITAT - private agency.
ACTDEC - accredit a small number of schools and were originally set up to accredit their own school; their independence is often called into question.
IATEFL - this organization does NOT accredit any school; if a school says they're IATEFL accredited they are lying.
College of Teachers - currently accrediting 1 TEFL provider.
ODLQC (Open & Distance Learning Quality Council) - private organization which accredits different courses (not just TEFL). They currently accredit 3 TEFL schools.
QCDA (Qualifications and Curriculum Development Agency) - former UK agency; closed now and no longer operates.
SQA (Scottish Qualifications Authority) - for Scottish based courses only; they do not accredit international courses. Official Website.