I dont know about the illegality of it, (although I seem to remember from my crime lectures years ago that you can cause criminal damage by administering a noxious substance) but my friend is a fireman, and was called out by concerned neighbours of a woman burning all sorts, including plastic, in her back yard! She wouldnt let the fireman in intially but they told her if they didnt, they could get police assitance to let them into the property.
Im guessing that it has alot to do not only with the substances you are burning, but also the size of the space where the fire is contained, and the proximity of others to the smoke. Maybe call your local fire service and ask them? They are usually pretty helpful, I say usually, some of them are grumpy whatnots!