The Society of Friends Quarterly Meetings are filled with all events for members that have been recorded in each separate regional meeting house. This covers deaths, births, marriages and transfers from one meeting house to another. This records are submitted by representatives of each meeting house at the Quarterly Meetings and are jointly recorded in the record for that quarter.
I know the records for certain regions in Canada are on-line. I believe I have an on-line resource for some English regions but off hand I can't remember the location. I will try and find it tomorrow to see if it covers your area of interest.
As to the IGI listing the girls and boys separately I don't understand their reasoning for doing that but I have found it done that way with some Parish Records as well.
Have you tried a simple google for "Society of Friends Quarterly Meetings/London/Essex/Kent?
I will check to see what area of England I have tomorrow.
Sorry I couldn't really answer your question.
dollylee