My online search into the London Teacher Training College suggests that its qualifications are approved/validated/whatever by St Clement's University. I value qualifications from that 'university' rather less than than I do the tissue with which I perform certain rather personal functions.
Now to practical matters.
1. If you have a BA in English from a real university (as opposed to the St Clement's type) you can teach outside your own country (though some form of teaching qualification may be a legal requirement in some countries).
2. In the TEFL/TESOL/ELT world, the initial qualification is generally the Certificate. Teachers who work towards the Diploma normally do so after (a) gaining a Certificate and (b) having at least one year's experience.
3. If you are serious about working in this field, then you should work for a Certificate in TESOL/TEFL/ELT. The most recognised/accepted certificates are the Cambridge CELTA (Certificate in English Language Teaching to Adults) and the Trinity College Cert TESOL. The Cert TESOL validated by the College of Teachers is also recognised by some. Other certificates may be accepted, but you need to ensure that the training leading to the award of a certificate involves a minimum of 100 hours of input and 6+ hours of observed teaching practice.
4. Be wary of online courses. Most employing institutions have no respect for a course which does not involve what I have underlined in #3
4. Master's degrees in Applied Linguistics/ELT are also a way into this field, especially if you wish to work in a university, or in the American part of the TEFL/TESOL world.