...meanwhile, back in the States...
Being one of those unfortunate children of the 80's, and growing up in Los Angeles, fueled on British Pop, I, too, have been publicly humiliated by my own "affected" faux-british accent. But after wandering into the folk music arena, I quickly learned you can't avoid it when you tackle some fiercely Scottish piece, such as "MacPhearson's Lament" or "The Bonny Shepherd Lad", or some jovial Irish tune like "Johnny Dhu", and I never received a comment that it sounded bad or faked.
I'll also toss into the fray that in the 7 years that I've been working the Rennaisance Faires around here, nothing has been more painful to listen to than the oh-so-incredibly-Ahmerrahcun renditions of "Haul away Joe" and "The Gypsy Rover". Call me a purist, but it is literally like nails on a chalkboard to listen to them plod through it. After someone finished mutilating "The Minstrel Boy", I damn near killed myself.
If you can do it well, go for it, it keeps the spirit of the song. If you can't, well, keep your day job... :)