Actually, I think that if you can get to the current fashion editor in person it would be best. I'd do everything I could to communicate directly with her.
Sometimes assistants and receptionists work as a "gatekeeper" ... which means that they are either told to or take it on themselves to "protect" the boss from random inquiries and things that can take up the boss's time. So, sometimes your "attachment" and email never even reach the person you wan't to impress ... if the "gatekeeper" decides that it's not important. It's always better to get past the gatekeeper and communicate directly with the person who hires, if at all possible.
So, since you have already been told that the Fashion Editor is the person who you need to talk to, I'd go back and just either call or email the company and ask for the Fashion Editor's name and contact info. Don't say what it's for, unless they insist. If you get it, attach a resume to a well thought out, but brief letter of introduction, stating the most impressive thing about why she should consider you for an internship and ask for a meeting ... and send it directly to the Fashion Editor.
Of course ... if the no longer have a fashion editor at all .. then you have to ask some more questions about who is in charge of the fashion dept., etc ... or if it's a small magazine, you can always go the the editor in cheif. Hey ... if you impress the top boss ... and he or she passes your resume down to someone lower, that lower person will pay a lot more attention to it.
If they still won't give you the editor's contact information thank them and tell them you will send it later. Then do some homework ... the name and contact info is probably on the masthead of the magazine or the website. If you get a name but not an email, you can try the receptionst again and just say, can you give me Jane Doe's email, please? If you use her actual name, sometimes they won't question you.
