iPad mini 3 bought from United States
No iPads have ever been network locked and all current model iPads with cellular connectivity support both CDMA and GSM networks (see Apple's LTE information), with no frequency limitations.

What that means is that your US-purchased iPad Mini should work just fine with an O2 data SIM (and any other UK data SIM for that matter - EE, Vodafone or Three). If your SIM isn't working, I'd verify:


Is it a data SIM? 
Does the SIM work in other devices (eg, try in a cellular dongle)