This is actually a different question from yours. Fanatic wants to plan to start working for Disney from the very beginning of his/her career, which has it's own answers.
My brother is in the process of doing that right now. He's interested in hotels and operations (rides), which is different from design, but his path might be of interest to you as well.
First, you can get your feet wet in Disney's College Program.
http://www.wdwcollegeprogram.com/sap/it ... index.html
Here's a UK site I found:
http://www.wdisneyw.co.uk/wdwcp.html
There aren't any design internships - you are basically just like any other hourly employee, but it's a fun way to spend a couple months (check out Lion's thread on his experience, and my brother had a blast), it shows Disney that you are committed to the company, and it helps you get to the next stage, which is...
Disney Professional/Advanced Internships
I can't find the link for them right now, but they are like a Super College Program. You are placed in manager type positions within the company and at the end, if you do a good job, you get a job in that capacity. Here's a link to the different type of internships that might be included (not sure though):
http://disney.go.com/disneycareers/coll ... ities.html