Update from me. My sons' passports posted 29/5, text confirming receipt 2/6.
Lots of panic from me as I saw the headlines, particularly since I hadn't noted the barcodes. Thanks to a helpful poster on here and a very helpful Barclays bank, got the barcodes from the back of my cheque (which cleared 9/6).
Called 0300 number on 16/6 who confirmed both were awaiting inspection. Called again on 19/6 to be told that they couldn't find passport numbers. Was promised call back. No call back.
Phoned Peterborough this afternoon on 0845 6015549. Got through in 17 mins and spoke to a lovely lady who confirmed that both passports had passed inspection and had been received by central printing today. We will get them this week, 3 and a bit weeks from posting.
The 0300 number is really only any use to find out which office is dealing with your passport. Its not their fault, they don't have access to the in information and the call back system doesn't work.
If your application is at Peterborough it seems to be working well and the number above will get you through (ignore the messages whilst you're holding).
It seems to be that the system works just fine providing you have included everything. The issue is leadership - inadequate planning for entirely predictable demand and resources poured into a toothless call centre designed to keep you away from someone who can answer your question and to complicate and elongate the process. And as for the barcodes, lady at Peterborough didn't even ask, she found me using name and postcode like everyone else on Earth.