If you have signal bars and working calls / texts, 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:
• Correct giffgaff APN settings: http://giff.ly/gg_settings
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 common solutions.