If I read the application correctly there are plans to accommodate 25 children at this nursery. I agree that nurseries are in short supply but I am not sure whether I would like this size of business next to my home so I can understand the objections. Its one thing living next door to a childminder, a medium size nursery, which this is , is something else altogether however I would suspect that the children would spend a lot of time in Horniman Gardens on fine days and you may actually not hear very much at all unless the windows are open or they are all outside at once which I would think would be very unlikely.
There are several precedents of detached houses in Forest Hill becoming nurseries- I can think of two immediately. The good thing is that arrival and finish times can be staggered so there may not be the 'rush' at the start and finish of every day.

As regards the concept of working mothers, as far as I can gather and from personal experience, most women, and indeed fathers want a good work/life balance. Staying at home full time is these days a luxury that few can actually afford despite the exhorbitant cost of childcare and not everyone is cut out for it; some make a good job of it by getting involved in their local community but for a lot of women it isn't so attractive. The fact is that children spend quite a lot of time in nursery and other childcare settings anyway and it is no longer the professional view that children are better off spending 100% of their time with their parents- its good quality care that is the main factor. Women who choose to work when their kids are small do it to keep their brains active and themselves sane, to have a life of their own hence being good role models for their particularly female children, and to keep themselves in the job market for the sake of future income and their pensions. Kids are, after all, extremely expensive to bring up- £200k according to a recent report and thats without the private education and designer trainers.

In respect of planning notices, this should be posted by the owner as soon as possible after the application. If the owner has not done this then you can ask the council to extend the consultation period ie start from when the notice is put up- a bit of an own goal as this can only delay the application going to committee.