There is no law saying that bonfires are illegal. However, Smoke from a bonfire (or any other process of burning) can be considered a Statutory nuisance and as such can be dealt with under the environmental protection act 1990. Your local Authority MUST deal with stat. nuisances, and this act states that the Local Authority SHALL serve notice to abate a statutory nuisance where they know or have reason to believe that a nuisance exists or is likely to exist. You will have to show that the nuisance is substantial though. In my experience, a bonfire more than once a month could be considered a stat nuisance is there was copious smoke which was causing you to shut windows. In fact, just the fact that you have to go indoors and cannot enjoy your garden is enough, but again, it would have to be quite regular for it to be considered a problem. Once every few months would probably not be considered a nuisance.