Hmm, it's not always 'up to London'. I've lived in a lot of different places and the ups downs and across's are almost universally linked to geography.
Anywhere south of the M4 tends to say 'up to London'.
Anywhere within about 1 hour drive tends to use the geographic position interchangeably with 'into London', with increasing use of the latter the closer you get to the city. This is also affected by commuter popularity and transport links. Cambridge seems to use 'into' more than its location would suggest for instance.
Those in the West like Bristol or Wales tend to use 'across'.
Birmingham is kind of the middle ground but from about Sheffield up its almost universally 'down' in my experience.
Having lived in Scotland it mostly just 'to', nothing about up down or across. You really feel the distance up there.
