Update (22/05/2014): No, I still don't have the unlock code... I did try fonefunshop as recommended by some people here but they got back to me very quickly with "Sorry, we can't get the code for you" and gave me a full refund. Ditto for another service called code-unlock-now.
However, I've just been speaking to customer services. According to them it's a team in India that deals with unlock requests and they're basically not doing their job. EE are bringing this service back to the UK as far as the chap I spoke to knows. Whether this is yet another excuse to fob me off or the truth, I don't know. We'll see what happens in the near future. Meanwhile I might well try politely e-mailing the addresses that were given further up in this discussion (going in there all guns blazing won't help however tempting it is).