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I thing, technically, it's downhill.
The magnetic pull of the Poles mean that the Earth is a bit squished from top to bottom. In other words, it's not quite a sphere. The Poles are, therefore, closer to each other that any opposite points of the Equator would be to each other. So the Poles are closer to the centre of the Earth that the Equator.
Therefore ... in the Northern hemisphere, if you walk away from the Equator, and towards the North Pole (ie northwards!) you are getting closer to the centre of the Earth.
So, if you walk from Brighton to Scotland, you are walking downhill.