I have a blue badge. Here how it worked last october
Disney, on property, will honor UK blue badges. You can park on disabled parking spots at all 4 theme parks.
Downtown Disney is another story, as it is "public access"
for every other location, you need a temporary (red) florida parking permit
you need to email the osceola tax office in order to get one
I didn't check the thread PP mentionned, but if you need additional info, just drop a line here.
edit : ok, lol, looks like I was involved in that thread too, lol
just to add that, while many parking enforcement "officers" will not frown upon a UK blue badge (outside of disney proprety) it might be best getting a Florida tag, as you may encounter the odd enforcement person who will decide that your badge is not valid (and they would be right by the letter of the law)