Going up to London fits badly with the vernacular in Aberdeen, and most of Scotland, when we say going Down South, ie, to England.
Do people in London say they are going Down to Aberdeen? Surely not!
That being said, few of the general public are talking from a tack and signals perspective.
Idiomatic usage does change, and we all know about how railways stick to their way of doing things. So what was common before 1830 may have been reinforced by everyone using the railways, but we've had two generations using them less and less and inventing new idioms based on their experience.
Newspapers can take us back a bit further than 1830, but not before 1700. I find "down to Scotland" and "up to London" are common from 1710. I suspect this has a number of sources: itineraries would be one (not just for stage coaches), and the notion of social hierarchy would be another.
As for Aberdeen, this from the Caledonian Mercury 23 October 1745:
A sloop is gone down to Aberdeen in order to bring up the members of parliament by sea, having been discharged to attend this sessions, by a proclamation published at Edinburgh.
The historical context is a bit complicated, since this paper supported the government and was based in Edinburgh. At this date, however, Edinburgh was controlled by the Jacobites, who were debating whether to invade England - the landing of a French force at Stonehaven (reported in this issue) helped to decide them to march to Derby and subsequent disaster. So I guess the MPs were going up to London, but who had proclaimed what in Edinburgh and when I have no idea.
Not only is there is nothing unusual about idiomatic usage changing, but you can get two incompatible meanings at the same time. Just talking about "up", there is the troublesome "up to". How about this, from NRE:
You can buy an Advance ticket for most journeys up to 12 weeks in advance, and up to 10 minutes before departure.
You can interpret "up to" in two ways (mainly; there may be others). It can be about numbers, in which case "up to 12" means 12 or less, and since weeks "in advance" count backwards in time here "up to" means "after". But it can be about dates (or times), and then it means "before" (i.e. leading up to), and "before 10 minutes before" does make sense. But if you interpret both "up to"s the same way the sentence makes no sense, does it?
It's a common problem when doing arithmetic with words (and doing algebra is even worse) - the rules of language and mathematics are different.