Yep, the application opens on June 1st. Have your personal statement ready, and apply early because it'll take a few weeks for AADSAS to approve your application. You can apply even if you haven't taken your DAT yet.
Something else you can do is use a letter of recommendation storage service, like Interfolio.com, to collect your letters of recommendation. It's way easier to ask your professors to get them done now than asking them in the summer along with everyone else who is applying.