I wouldn't recommend going through the network. Sure, you get £25/£30 calling credit etc. on top of your unlocked phone, but you may have to wait a while for the unlock codes to be sent... about 2 weeks usually and there's no guarantee it will work. I was waiting over a month for my Vodafone to unlock.
Chances are, you will grow fond of the new network, end up with 2 phones, will need to topup your primary phone (when that runs out of credit), thus, in the long run, you've wasted time and money.
Find a nice little phone shop, pay £4 and avoid so much hassle.