The blizzard site is reporting that the Euro closed beta will be starting at some point later this month, those chosen to take part will be notified by email a couple of days before the beta begins.

Extract from the blizzard site:

Over the past few weeks, our growing European teams have been striving to prepare the technical platform to support the beta test, and we are now in the final stages of implementing the required technology. It is our intention to post an announcement very soon that indicates the specific date in September when the European World of Warcraft closed beta test will start. Under the current schedule, the first wave of selected testers will be notified by e-mail a couple of days before the Beta launch. Thank you for your patience, and we hope to have you playing World of Warcraft as soon as possible!