I am travelling geographically down the country from north of the city of London. Do I state "I am travelling down to London" or do I state "I am travelling up to London" in reference to its capital city status?
There are many traditions, with altitude being a pervasive influence (up river / downstream, up in the hills / down to the sea), and latitude also being a common factor, particularly in the UK (oop north / darn sarf [sic]).
Where these traditions conflict, it would be rather zealous to complain about any preference expressed.
Of course, you can avoid any uncertainty by restricting yourself to "I am travelling to London". To my ear, up and down sound more natural when accompanying the verb to go, rather than to travel anyway.
Well technically, up or down have no real meaning in this context, as they do not imply a direction.
The use of the words downtown and uptown, usually refer to the condition of the area, the class of it. In London as a colloquialism, many people say "I'm going down town", meaning going to the city, Westminister, or anywhere within Zone 1 of the underground really. Then again I have heard people use "up to town" meaning London as well.
When there is significant distance involved, it tends to be up in my experience.
Occasionally, though not often, people do think that the difference is akin to heading North (up) and heading South (down); though I believe that is a less common interpretation.
TL;DR: No fixed meaning, you can go up or down to London apparently from anywhere in the country. Preferably try to use compass directions.
It's always up to Oxford or Cambridge wherever you start from. This might indicate that it's up to somewhere impressive or desirable (which London would be to a railway company, at least). Whether the capital is one of those places depends on your view of the country, I suppose.
Also, on many Caribbean islands, 'Above' or 'up along' is on the windward side of the island, usually but not always the west. Not sure if that helps, but it's interesting.
I was led to believe that you always went UP to a Capital and DOWN from it. but you can go up the pub, down the pub, down the shops, up the shops etc. The Capital instance - along with the Oxford Cambridge one - is the only one that is an etiquette or protocol type thing, the rest is just what you feel like at the time, and you have probably said it before you've even noticed.
Based on living fifty odd years in and around London —
In general, a Londoner will talk about going "up" to a more northern area of London or somewhere further north than London, and "down" from such a place to London. Going anywhere else out of London else is often "down", and again it's "up" from such a place to London.
We even use "down" in a more general way when going anywhere from our starting position, e.g. "I'm going down the shops". But, confusingly, we'd never say we're coming back "up" on the way home :) This usage is very informal.
There's also a slightly old-fashioned expression "up west" which means "to the West End of London [from some other part of London]", especially in the context of visiting that area of London for entertainment.
Edit: I've also heard all of the examples Orbling mentioned. Some of these usages are more variable than others and hopefully our experiences show that these aren't hard and fast rules.
going up to London is the saying from many years ago no matter what direction you are heading from. this is simply because it is the capitol. so up town in your own city from north,south, east or west. you are going uptown. hence London is the capital of the England so there for you are going uptown no matter what direction you are heading from..
If you're from the South of England, you will always go up to London. If you're a Northerner with a chip on your shoulder, you will make a point of saying that you're going "down" to London and argue the toss if anyone from the south tries to correct you. Up to London is traditional which is why the railways use that convention.