Don't mind if I do!

Don't Mind If I Do was a catch-phrase popularised by Colonel Chinstrap in the radio programme It's That Man Again. It means "thank you very much, I am pleased to accept your kind offer".

It is chiefly used in accepting the offer of a drink (well, that's usually when I use it, anyway), but will do for any other small gift.

This is said to politely accept an offer of food or drink:
"There's plenty more cake if you'd like another piece."
"I don't mind if I do."

Beginning in 1910, and then especially by the late 40s, this phrase was a very popular British way of accepting an offer - meaning "Yes, please!"

[I've summarised the gist of the article in A Dictionary of Catch Phrases here.]

To me, it now sounds a bit quaint and old-fashioned, maybe even with a tendency towards lower class. But this is a purely personal impression.