Teaching English as a foreign language is very different from teaching secondary English. The skills are only partially the same. I have known a number of teachers of secondary English fail when attempting to teach EFL.
I am not certain you are qualified to take DELTA as, if I remember correctly, it requires you to have 1,200 hours of teaching English to adults in order to be eligible. Also I'm not sure whether or not that experience needs to be in an EFL context. If you want to work in universities I would advise you to do the MA TEFL which in any case includes much of the DELTA. If not, then CELTA or Trinity TESOL. There is a general shortage of EFL teachers so finding work is not usually a problem.