I don’t recall the exact wording of the joke, but I remember thinking when I saw it: “that would make more sense if she said ‘…we’re wearing clean underwear.’” My interpretation is basically the opposite of Miss Mapp’s: If they got into an accident it would be OK because their undergarments are properly modest and ladylike. Or, that it would be OK because their underwear would keep them warm while waiting for rescue.
Either way, it’s not funny.
The exact wording of the joke is what I posted.
It doesn’t linger on it. It pans a bit and zooms in on it.
But you’re probably right in that it means nothing.
I just thought the long underware was about it being cold outside.
Miss Mapp is correct. Lloyd basically says that he doesn’t intend to have an accident, and Margo replies: “It doesn’t matter whether you intend to or not. We are wearing long underwear.” Two sophisticated NY ladies would not wish to be caught unawares in utterly unglam underwear.
I’ve always chuckled at the dialogue myself, since it not only amuses to think of la diva Margo in red flannel undies with a flap in the back, but also it’s a cute moment that breaks a bit of the tension lingering from the previous scene (the argument between Margo and Bill).
Understandable - after all they’ve both been dead for three hundred years 
[channeling Margo Channing]
All painters should be dead for three hundred years!
[/end channeling]
Every character in this movie is gay-by-default. This picture couldn’t be any gayer if it were reshot by John Waters from an Armistead Maupin treatment. 