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I would like to create a distance matrix and have as output the distances expressed as kilometers (km).

Here my current output, which I believe is in degrees and NOT in km:

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My coordinate system (CRS) is EPSG:27700, OSGB 1936 / British National Grid, I am working with an Apple computer on QGIS 2.14

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The unit of EPSG:27700, OSGB 1936 / British National Grid is meter, which means the distances you got are in meter. You need to divide by 1000 and you will get the distance in km.

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