Unlock iPhone for different carrier
The only way to do this in a supported way without jailbreaking the phone is to have O2 do it. There's simply no other way. They have to send a carrier update to the phone which unlocks it.

If you want it done faster, I would recommend returning the phone if you can and purchase an unlocked one straight from Apple.

I don't know how UK law works, but in the US, carriers are required to unlock your phone if you have no financial obligation to them for the device. Any phone you buy directly from Apple won't have any kind of carrier lock on it.