Only the carrier it's locked to can arrange an unlocking, so if you got it originally from Virgin then they should be able to do it for you relatively quickly. If not then there's still a chance that VM will help but what you might have to do is contact EE and ask them.
Why EE? Well Virgin Mobile is actually what's called a MVNO (mobile virtual network operator), they don't really have their own network but piggyback (if you like) off of EE's. So strictly speaking the phone is probably locked to the EE network.