In Downton Abbey, they are constantly mentioning going "up to London." However, this is supposed to be set in Yorkshire, which is WAY north of London already. So, why don't they say they are going "down to London"?
This is down to the normal English usage that you always go "up" to the capital.
It has always been the convention on the railways that all trains heading towards London are "up" trains, those heading away are "down" trains. This usage is common to all transport.
Up and Down are not related to points of the compass, but have always been related to the relative status of your destination. It has always been the case that you go "up" to a destination with at higher perceived status than your current location. For example, students always go "up" to university and come "down" from it during the holidays.
According to The Phrase Finder:
Do you say 'up to London' regardless of which way you are coming from and if so why?
This is an odd one. The widespread, if a little archaic, use of 'up' when travelling to London is based partly on the importance of the capital and partly on the habit of denoting railway lines as 'up' lines (to London) and 'down' lines (out of London).
Google NGrams shows that "up to London" was many times more popular than "down to London" in the 19-20th century, the time period when Downton Abbey is set (although since then the gap has closed a lot).
Cheenmunka has it mostly right. You always go "up" to the major city, and "down" to the lesser city.
This convention is actually from the railway.
In British practice, railway directions are usually described as "up" and "down", with "up" being towards a major location. This convention is applied not only to the trains and the tracks, but also to items of lineside equipment and to areas near a track. Since British trains run on the left, the "up" side of a line is on the left when proceeding in the "up" direction.
Today, rails don't run like this, and therefore it has been dropped out of popular speech (hence all the comments on Cheenmuka's post), but back in the time when Downtown was set, it would certainly be more widely accepted.
This has been carried elsewhere in the world. For example India