Why did your application fail?
Although it can't hurt to have some classroom experience, having TEFL experience is less useful than you might think when applying to train to be a school teacher back in the UK. For example, it doesn't count as equivalent to volunteering as an assistant teacher when applying to be a primary school teacher, even if you have been teaching that age abroad.
As you might end up having to do TEFL in the UK when you first go back, you should definitely choose Trinity CertTESOL or Cambridge CELTA. It doesn't matter too much which centre you choose as long as it is one of those qualifications.