Does 在伦敦的南面/南边 is a mixture of in/on/to the south of London?
Well to distinguish the south-side of London (within) and south of London (outside):
在伦敦的南部/南方/南区/城南 The south-part/side/district/ of London.
Note: 城南 is specifically the south side of a city. 在伦敦的城南。
在伦敦的南边/南面 South of London. Outside of London.
I feel 南边/南面 could be used to mean either inside or outside depending on the context.