Reading some forum pages about the meaning of the phrase never mind, I realized that there's a difference in usage of it, between American and British English. What's the difference in meaning of this phrase in American English and British English?
Considering @Snubian's answer, I think the phrase could be used both ways in both regions.
I don't see a particular UK/US distinction; rather, the difference depends on the mood of the speaker, as @Jez suggested.
I do notice a difference (but again, not a regional one) between transitive and intransitive use:
Transitive = Disregard
Fred: I'm slightly worried about X
Bill: Never mind that - what about Y?
Intransitive = "Oh well, that's a shame, but let's not worry about it"
Fred: So I'm afraid we'll have to have pizza, not tacos
Bill: Never mind. I like tacos.
It is possible to detect a subtle difference between typical usage in the UK and US.
Bill: Hey, Fred, how would you like two free tickets to see Michael Bolton?
Fred: Yeah, sounds cool! When's the show?
Bill: Saturday night.
Fred: Dang, I can't make it Saturday, I'll have to pass on the tickets.
Bill: Aw, too bad.
Fred: Never mind.
Fred: Hey, Bill, do you have those two Michael Bolton tickets you promised me?
Bill: Oh, Fred, sorry mate, but the missus gave those to her sister.
Fred: What?! But you promised them to me!
Bill: Yeah, I know, but ...
Fred: We've hired a babysitter and everything!
Bill: I'm really sorry, Fred - look, let me make it up to you ...
Fred: Oh, never mind! [storms off in a huff]