Verify your giffgaff ‘Roaming Status’
Note this is a giffgaff account setting and not a phone setting.
Is it ON or OFF?
Next, do you first have signal bars and working calls / texts?
If yes, then it's likely your phone is not correctly configured for mobile data abroad.
For mobile data abroad, you need ALL of the following phone settings:
• giffgaff APN settings, see this guide
It’s likely that your phone has the O2 APN which works for data in the UK but not abroad. It must be the giffgaff APN for mobile data abroad.
• Data roaming turned on. Note this is a specific phone setting and is usually turned off by default.
• Mobile data turned on.
Specifically check the APN and 'data roaming' settings, as these are the most likely solutions.