Those particular locations are quite close together in latitude, so you might be excused if you did not take into account the curvature of the Earth. However, if you were to take south-west England to Edinburgh, for example, then the distance in latitude would be enough to matter. The difference for the particular latitudes you show is about 0.11 miles per degree of longitude; between London and Endinburgh would be about 4.3 miles per degree of longitude.
Because of this, because you are working in areas where the curve is likely to make a difference, you should be using Great Circle distances.
