We received DC's first passport this morning. What a relief! Yesterday I couldn't take the stress any more so I contacted Paul Pugh's office again, within hours someone in the passport office was looking at the application and today I have it.
I don't follow the logic of them waiting until days before travel, what if there is an error or counter signatory is unavailable. They quote up to 6 weeks for child's first passport. It shouldn't be 5 weeks of the application collecting dust and then a couple of hours work gets you a passport.
For those of you interested in timeline:
Posted child's first passport application to Liverpool end of May
Fee taken from card 2nd June
Text confirming receipt 3rd June.
Text stating passport was being printed 2nd July at 9am
Received passport about 11ish on 2nd July
I'm certain it would have taken longer had I left things to run the normal course. My advice, email MP, Paul Pugh, don't wait for callbacks (either 0300 or upgrade team). The upgrade team never called me back. I called the 0300 number everyday for over 2 weeks. What really got it moving was emailing Paul Pugh's office.
Best of luck to everyone.