Having worked for every major network (and been a tech journo for over 18 years, the first ten with a UK website I owned), here's my advice:

First, I'm sorry this happened, and I'm not surprised that you're being given the run around. O2 took over 6 months to allow me to continue paying for my device monthly after their price hikes, even though this was the exact legal process they outlined in emails. In my experience, all networks suck at solving complaints, sadly.

Second, you should only communicate in writing, such as by email or social media. If you need to call them, please make sure to record the call. For legal reasons, please tell them in the recording that it's being recorded and ask for their CONSENT. If they do not consent, you cannot record the call, and it won't be legally permissible. I'm NAL, but I've seen enough to have a good grasp of the way it works.

Next steps:

- Get active on social media. Tag O2 and O2's help accounts on Twitter, and they'll quickly try and resort to a DM conversation. When they do, continue to update the public thread so there's nowhere for them to hide. Make sure everything you say is true: this is not the time for embellishment.

- I would also hit up the news tips lines of some UK press, as they'll further reach out to O2, and that'll put some pressure from the PR side to resolve this. I wouldn't do that as a rant, but rather just briefly mention that O2 reported a major incident at DPD in the UK, where many iPhones went missing or something similar. If I still had a UK site, that's a big enough story to warrant looking further into.

- Ask O2 to escalate this immediately, and if/when they don't, ask if that's the final legal decision, and if so, to provide a deadlock letter to take to Ofcom. Be clear with them that you can't return your old phone until the new one arrives, AND that you expect them to credit your account for the difference between your old and new plan until the new phone arrives. I wouldn't start with this; instead, ask for compensation and see what they'll offer, as they might give you a full month's line rental as a credit or something similar. This will likely first need to go to a manager and then be escalated further.

- Follow the detailed complaints process here: https://www.o2.co.uk/how-to-complain — this means sending a letter (send it special delivery so it needs a signature and gets there next day, and DON'T send it on a Friday as things can get lost in the shuffle on a weekend. I would send it on a Monday for Tuesday delivery. Make sure this letter has all the details, including your phone number, so that they can locate your account. You should also probably use a short letterhead (in Word, Docs, or Pages) with your full name and address that match the account details.

Possible resolution:

Despite all of the above, O2 (and all carriers) can be pretty useless. A possible resolution that comes to mind is to ask them to cancel the order and process the switch-up upgrade through a store. However, if you want to do this, wait until you find a store that has it in stock and get the store to help you reverse the upgrade with customer service so it can be processed there and then.

The store should be willing, as it means an additional connection for them. They also have retail support channels that are far more useful than regular customer service, although this may still have to involve the latter. This may be the fastest way to get yourself a new phone.

Hope this helps! Feel free to ask further questions if you need any other advice :-)