Ensure you have the correct APN/Data settings. You need to set-up your handset with APN settings before you can use the internet or MMS with the giffgaff network.
As you haven't stated the mobile device you have, please follow the link below to find settings for the most popular handsets including iOS(iPhone, iPad), Android(LG, Samsung, HTC), Nokia Lumia(Windows) etc. http://community.giffgaff.com/t5/Using-giffgaff/Force-the-change-of-SMS-settings/ta-p/4871794
guide that allows you to select the network manually.
Please try reconnecting by switching "Flight mode" On and back Off ("Settings" > "Flight mode"). This resets the active connection.
If you’re still having problems, then you can try turning your device off for a couple of minutes and on again to see if that helps.