What they mean by "you need to have a standard of education equivalent to that required for higher education" is A-Levels, those extra two years of education which prepare you for university. A degree is not necessary at all. Basically, CELTA course centres prefer that candidates have this level of education, however, like Briona said, they'll give you a little English test and a maths test (which is easy), so don't worry.
If I were you, I'd go and have an interview, talk to them and you'll see that it's probably nothing to worry about. I did the CELTA straight off! :)
Good luck :)