You can also use the webchat and just ask them which office is processing your application (link below)
https://www.gov.uk/government/organisations/hm-passport-office/contact/hm-passport-office-webchat
I applied 29th April, was left in ‘identity details received’ I fly 12th July so called the mainline using the options mentioned by jomc2571 on 27th June and then emailed the upgrade team for where my application was processing and my application was approved 2.5 hours after my email, printed 29th June and i just received it today (30th June) around 12:30pm.
NOTE: when you speak to an advisor on the phone advise them you need an urgent upgrade and tell them how many weeks ago you applied and when you travel. – they will not give you the upgrade email. You need to email them unprompted and supply them with a PDF of your travel document this has to show your name on and date of travel and the below info:
Subject line of email should be: URGENT UPGRADE: Travel DD/MM/YYYY
Full Name:
DOB:
Contact Number:
Email address:
Application Reference Number:
Date of Travel and Proof of Flight (actual PDF not a screenshot):
Last day able to collect passport:
The upgrade emails addresses all have the same format for example Peterborough is: PeterboroughUpgradeTeam@hmpo.gov.uk
Keep in mind they are case sensitive so copy the above format for whichever office is processing your application.
I hope this helps 🙂