Update 2: O2 has mentioned that the issue is now fixed, and that an OTA update with the passive-listening feature enabled will be made available soon:

We're trying to get the updates out sooner by streamlining the test and approval process. As a result, we were trusting Microsoft to test the O2 software updates for us and provide the results of the tests for us to approve, rather than us testing it, releasing back, and waiting for it to be pushed. In the case of the Lumia 930, the Cortana issue was missed by Microsoft, so we will be working together to improve the process for future updates. Microsoft have identified the issue and have fixed it - as a result, the previous 930 update has been put on hold until it's replaced with the fixed update which we hope will go out soon, though no ETA has been provided.

Update 1: Chris from O2's social team commented on the omission of the "Hey Cortana" passive-listening feature, stating that the carrier was looking into the issue:

Everybody, I'm sorry I didn't give a heads up that the Denim update for Lumia 635, 930 & 1520 would be going live last night - I received notification that this would be going live yesterday. It was a day off and I was unwell so hadn't seen it until today. I understand many of you are unhappy around an issue with Cortana functionality being missing - please leave this with me and the device team, we'll find out what the issue is and report back.

Original story follows.

UK carrier O2 is rolling out the Lumia Denim update for the Lumia 930, but it looks like the "Hey Cortana" activation feature is not available. While there is no statement from O2, several users have taken to the carrier's forums to complain about its omission.

The "Hey Cortana" command utilizes passive-listening technology found in Qualcomm's Snapdragon 8XX line of SoCs to invoke Cortana by speaking the activation phrase, even when the phone is in standby mode.

At this stage, it is unclear as to why O2 did not include the feature in the Lumia 930, seeing as how the UK carrier's variant of the Lumia 1520 comes with it. We'll have more to share as we find out what's going on. In the meantime, let us know if any of you on O2 are seeing the feature on the Lumia 930 after updating to Denim.

Source: O2 Forums

Thanks to everyone who sent this in!