@emma123 did you apply on Monday 13th July? I think that you might be alright for 16th August if you’re lucky, the average time now for an adult passport renewal is 23 days (not sure about child’s). If you’re worried and you booked your holiday before 23 March 2020 (and can send proof) you can call complaints and ask them to expedite your application. It might help.
You should be receiving emails and/or texts with your timeline. I just typed them out from there.
