I would call and make sure the SIM they gave you is the correct one.
Yes, GiffGaff runs on O2, and the GG users are HEAVILY restricted in favour of O2's own customers.
Some good news for me, O2 seem to have done something about my complaints about the Malvern transmitter; I recorded speed averages of 1.29Mbps last night, with a peak of 5mbps (d/l), and ~1mbps u/l (5 bar H+)
It doesnt sound like much, but it is (almost literally) a million times faster than the 0.02mbps we have been getting for the last five years