Also discussed here on WR.(I'm) delighted to make your acquaintance.
Fig. I am very glad to meet you.
Tom: My name is Tom. I work in the advertising department.
Mary: I'm Mary. I work in accounting. Delighted to make your acquaintance.
Tom: Yeah. Good to meet you.
Fred: Sue, this is Bob. He'll be working with us on the Wilson project.
Sue: I'm delighted to make your acquaintance, Bob.
Bob: My pleasure.
As for the people that might say it (very rare) I'm not 100% sure if they would make a distinction between thinking they will be seeing them again in the future, or if they know they won't, I personally think it became a crystalised expression and was(is) used as a declaration to say when you meet someone (regardless of future intention, it's just a formal statement). These types of things (i.e. what you say when being introduced to somebody for the first time) have the characteristic of becoming quite idiomatic.Main Entry: meet
Part of Speech: verb
Definition: come together, convene
Synonyms: appear, assemble, be introduced, be present, be presented, collect, congregate, converge, enter in, flock, foregather, gather, get to know, get together, join, make acquaintance, muster, open, rally, rendezvous, show, sit
I'm not sure if that indicates a strictly British (old fashioned) usage though..You can hear the accent by listening to many famous people: Wayne Rooney, John Lennon, Steven Gerrard or the comedian Jimmy Tarbuck. And here for you all to enjoy, are a quick list of Scouse words “ with a Queen's English " translation next to them:
The Words Da Werds
Ullo dur! Greetings! Pleased to make your acquaintance
Darrafact? Is that true?
Binbagged To be asked to leave by your boy/girlfriend