My wife works in Walthamstow. I think it's fair to say that she doesn't feel safe in the area. I've been in the area and it seems to be far more rundown than nearby neighborhoods.
I have a co-worker who has lived there for the majority of his life. He has been mugged twice in recent years, after going 30 years without any problems whatsoever. In his view, the large number of Eastern bloc immigrants are ruining the area. That's his view. Another co-worker lives in Leytonstone and doesn't seem to mind it. He is a family man and doesn't go out at night.
Even in the area we live in, my wife won't venture out alone in the dark. It's mostly about being smart and looking the part.
If you are looking in this general area, I would advise looking closer to Wanstead and further out from there. I used to walk about half a mile from Newbury Park tube station in the dark and never felt as uneasy as walking around in broad daylight in Walthamstow or Leyton.
The areas you mentioned are not awful, they're just not something I would consider. If you are away from the high street and council flats, there are some nice neighborhoods.