Regarding EE's unlocking policy: if you buy an off-contract device from EE or their "indirect partners" - which I'm sure includes Carphone Warehouse! - they state
here that they will unlock free of charge if you have a pay as you go account with them that's fully up to date. There is no requirement to wait 6 months. I would advise going to your nearest EE store and asking them to do it, I'm sure it will be very straightforward. In my experience EE unlocks take three working days.
Regarding Three: this is a grey area to me because if a phone is set to lock to its first network (like Carphone Warehouse phones are), and Three
doesn't lock phones, then couldn't this happen:
- Buy Carphone Warehouse phone
- Insert Three SIM and wait 24 hours (this is how long the first-SIM lock can take)
- Three doesn't lock phones so the phone remains in an unlocked state
- Insert other SIM, e.g. EE
- Phone becomes locked to EE
I'm not sure if that's how it works, but I would avoid the Three method for that reason. Most people advise buying phones from Three (or Giffgaff) because they sell them unlocked, but using a Three or Giffgaff SIM to effectively make a lock-to-first-SIM phone an unlocked phone seems like a risk to me - especially if the main network you use is one with a very awkward unlocking policy, like Vodafone!