In a recent blog, the question was raised when objections against sentences starting with a conjunction were first formulated, and one of the commenters, Steven Leefers, suggested it must have been around the Interbellum. So thanks to Steven for sorting this out for us.
Another reader of the BtheUnb blog brought the blog World Wide Words to our attention, which, five days ago, posted a comment on starting sentences with initial and. The verdict is: yes, it is possible to do so. Again, we are interested in your feedback, because we suspect that acceptablility may very much depend on context:
Bridging the Unbridgeable 
Oh no! Sorry, I misread the last option in your poll – I meant to say ‘acceptable under any circumstances’, as in, all of the above! I can safely say this (at least for myself, anyway), because I found myself starting a sentence with ‘And’ in an academic paper yesterday, and it was a perfectly lovely sentence if I do say so myself ;-)