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If you still have an old network profile in your settings you need to remove it as it can cause these problems.
For iOS 6 Goto Settings> General> Mobile Data>
Scroll to the bottom to see the profile and delete it. You may need to re-enter the giffgaff settings manually afterwards.
There are also some iOS 6 issues with wifi. I'm having problems with the weather app and connecting to the app store when on wifi. When on 3G they connect no problem.
Apple are currently beta testing the iOS 6.01 update that will hopefully fix these issues.