I used the Widened Lines five days a week in the late 1960s, travelling between Palmers Green and Farringdon because I worked in Farringdon Road. The service I used was a peak-period-only service and did not, I believe, run at all at weekends. The rolling stock, locomotive hauled, was well maintained but ancient compartmentalised carriages.
All on line now :A good starting point would be a Bradshaw guide - various libraries will have them for study.
The project for the extra connections was the complex junction linking the original New Cross-Lewisham-Woolwich line to the Nunhead line which was installed in 1929.Heyday for the Widened Lines - as they were - was the late Victorian-Edwardian era.
Services using them (not that I'm an expert) were - in summary:
Goods: Cross London Transfer from the Midland and Great Northern to the South - in particular onto the SER (via Metropolitan Junction and London Bridge: the Southern Rly had a 1920s project to put in extra connections in the Lewisham area to permit this to be rerouted via Elephant & Castle and Peckham Rye)....
I went all day Saturday! fortunately for not feeling overly aged I think they still do it.(alas I'm of the age that we even went to school on Saturday mornings!).