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This is usually a problem with the iPhone itself, or more specifically, with iMessages. If you do the following, it should sort the problem for you.
Goto Settings/Facetime/facetime and turn it off and
Goto settings/Messages/iMessage and turn it off
Now turn iMessages back on. The phone should now do some technical voodoo and recognise your new number. You can verify this by going to -
Settings/Phone/My number and checking it's now your proper giffgaff number.
You can now turn Facetime back on too. Just reboot your phone and that should sort it.
Hope that helps