Update: Working fine for us from London. We signed in to the PlayStation Store and even fired up Black Ops multiplayer just for kicks.
Update 2: We're now seeing error "80710D36" occasionally when trying to access the PlayStation Store, presumably due to congestion. We're seeing this from both London and New York.
Full PlayStation®Network Services Restored; Music Unlimited Powered by Qriocity™ to Become Available on PlayStation®3, PSP® (PlayStation®Portable), VAIO and other PCs
Sony Computer Entertainment Inc.
Tokyo, June 2, 2011 - Sony Corporation and Sony Computer Entertainment (SCE) announced today that Sony Network Entertainment International (SNEI, the company) will fully restore all PlayStation®Network services today June 2, 2011, in the Americas, Europe/PAL territories and Asia, excluding Japan, Hong Kong, and South Korea. The company will also resume Music Unlimited powered by Qriocity™ for PlayStation®3 (PS3®), PSP® (PlayStation®Portable), VAIO and other PCs.
Details of "Welcome Back" package program offered to all registered PlayStation Network* and Qriocity account services will be announced from each region.
Announcement for restoration in Japan, Hong Kong, and South Korea as well as for the remaining services on Qriocity will be made as they become available.
* Only available for those countries and regions with access to PlayStation®Store.