Hi Aidan
We’re in a similar situation. Applied to renew my daughter’s passport on 8/5/22 and HMPO confirmed supporting documentation received 16/5/22. Just gone over the 10 week deadline so applied for application to be expedited 2 days ago. No info about when it’ll be dealt with and we’re due to be travelling in just over 3 weeks. Spoke to advice line and was told I’d have a text and email within 48 hours of my request to expedite but have heard nothing. I rang again and was told just to sit and wait it out with no guarantee that it’ll be sorted in time.
Applied from London and application apparently with Belfast.