First child passport received today (17/07). Peterborough office.
Thanks everyone for posting their experiences, it was really helpful!
Full timeline and details below
Delivered by TNT 17 July 2020
Passport printed and sent 15 July 2020
Application approved 14 July 2020 (emailed and sent DM on Twitter as seem stuck after new photo was sent. Inquiries team asked for proof of travel dates and booking dates)
New photo received 9 July 2020
Photo rejected 9 July 2020 (emailed MP earlier that week)
Application being processed 25 June 2020
Documents received 22 June 2020
Documents sent 13 June 2020
Application received 13 June 2020
Identity details received 13 June 2020
Email sent to person confirming your identity 13 June 2020
Ask someone to confirm your identity 13 June 2020
Application submitted 13 June 2020