If this isn't a knife sharpener, please let me know what it is. It could be to sharpen razors. The spaces are rather narrow for a knife blade. It is made by Sky-line in Burnley England and has a whole list of patent/registration numbers on the bottom. It has a painted wooden handle and the rest is steel. This is a very solid piece. My guess is that this was made in the 1930s or 40s.
The following information was sent by a reader:
"I have one of these 'kitchen tools' and have always used it as a knife sharpener for my bread knife and other large knives. It was always to be found in my mother's kitchen drawer and when she died I claimed it. She married in 1936 so I think you were right with your dates."