Had my passport replaced two weeks ago by the normal route. Online application and photo submitted Thursday morning and a new passport arrived the following Thursday. It might be the passport offices are quiter as everyone plans to renew when they can get a blue one. Maybe.
The system does a good job of letting you know what is happening. They acknowleged receipt of my old passport on the Monday 8.32 although it had actually been signed for on the Friday. The application and photo were approved on Tuesday 20.02 and the new passport was sent out Wed 10.08.
Haven’t cleared the text messages yet!
Child passports coming for us in the past have usually only taken slightly over a week, using the regular route.
Good luck!