Essentially you will need a degree and a TEFL Certificate. You are right in that CELTA is arguably the best qualification, but it is an advanced course and I would personally not recommend it to anyone who does not have at least 2 years experience teaching along with a thorough knowledge of the English language.
Students who have taken CELTA have said it to be the most academically challenging 4 weeks of their lives!
For a full breakdown of qualifications you can see here
but in your situation I would suggest a basic TEFL Certificate and then go and teach abroad for a few years to get some experience. If you then still want to return to the UK you'll be in a good position to find a great job.