I know that it’s common in British English to say things like
You go on ahead. I’ll catch you up.
That usage is never encountered in American English. We would say, “I’ll catch up with you.”
In American English, the only use of catch someone up is in things like
I’ve been home in bed with the flu all week. Could you catch me up on what’s been happening at work?
where it means bring someone up to date by informing them of recent developments.
Do the Brits use this latter sense too?