Dear British writers:

"To catch [someone] up" and "to catch up with [someone]" have distinctly different meanings in American English.

If someone else has gone on ahead, and you are going to meet them sometime later, that's "I'll catch up with you." It indicates that you will be leaving later but traveling faster, in order to close the distance between you. It can also be used in a metaphorical sense between two people who intend to meet casually at some other point later, and in this case it means "when we see each other, I'll want you to tell me what's been going on in your life since we met last".

If you have gone on ahead, and someone else is going to meet you sometime later, that's "I'll catch you up." In this case, the phrase has nothing to do with traveling per se, but rather indicates that when the other party catches up with you, you will then catch them up by quickly explaining what has happened in their absence, so that you all have the same information with which to work from that point forward.

The extent to which this makes the Americans' brains twitch when you mix them up is somewhere between what your brains do when someone talks about 'lifts' and 'lorries' in an American accent, and when an American makes a valiant but horribly doomed attempt to figure out Cockney rhyming slang. It's not going to elicit as many snickers as when you tell the Americans that you "got off with" a girl in full view of the rest of the party, but it's likely to be far more confusing.

P.S. - We can all tell that Nicola Bryant isn't American. We always could. She tried very hard, and the parts she did get are correctly New England-y. Hugh Laurie is dead on, although he was not using the accent from New Jersey, where the show was set -- House's accent is Southern Californian, which is one of the most commonly used on television. There are several shibboleths, most notably the flat middle vowels when he pronounces something to be "cool".