I'm not familiar with the first phrase , especially not with that meaning. I wonder if perhaps it's similar to RUB UP AGAINST, as in a cat rubbing up against your leg. However, a little googling shows me several online dictionaries that contain the meaning you've listed. It seems to be a British English usage.
With the second phrase, at least here in the US it's more common to hear BRUSH UP ON xxxx. Maybe I need to brush up on my British English ;-)