There is no law against having an occasional bonfire but action can be taken against people who cause a statutory nuisance with bonfires.
Generally, for such a nuisance to be seen to occur the smoke or odours from the bonfire would either have to affect other people's premises to such an extent that normal use and enjoyment of those premises would not be possible, or to be damaging to their health. The council can investigate nuisance bonfires for you, but it is extremely unlikely that a one-off bonfire would be classed as a statutory nuisance
However, if smoke drifts across the highway where it causes or could cause an accident, this is an offence under the Highways Acts with a maximum penalty of £5,000. Additionally there is the possibility of facing private legal action for damages by people who suffer loss or harm as a result.