SOME carriers do charge more  but mostly they shouldn't.  A little extra to cover ferry charges to the islands is acceptable, but not for mainland deliveries.

I have sent a 4x4 towbar from the north of Scotland to the south of England for £10.  It arrived the next morning.

The carrier leaving London will only go as far as perhaps Manchester where they will transfer parcels to another courier who will perhaps go to Glasgow or Edinburgh where the same will happen again with a carrier from here.  It works in both directions.

I don't think anybody tries to get away with charging more for goods going south.  Perhaps they should.

PS. Scotland will still be part of a United Queendom.  James I of England (VI of Scotland) inherited the throne of England from his cousin Elizabeth I  so we share a Queen - unless she decides to move here permanently.