Check your settings,
I'm sorry to imform you but you don't actually need the BBM add on for IPhones as it's free.
The reason for it to not working over Mobile data is because you need to insert giffgaff APN settings on your Iphone.
You can automatically change your settings by texting the word settings to 2020, if that fails follow this short guide :-)
MMS Proxy: 184.108.40.206:8080
MMS Max Message Size: 2097152
To manually change the settings above go to...
Settings>General>Network / Mobile Data>Mobile Data Network
Once that is done go to...
and check that "MMS Messaging is turned ON
Please note: MMS messages cost 16p to send and it not covered by your goodybag.
If still nothing then turn your flight mode on and off.