Advice from the National Society of Allotment and Leisure Gardeners.
Under the Environmental Protection Act 1990, it is an offence to cause a statutory nuisance. This includes smoke, fumes or gases "emitted from premises so as to be prejudicial to health or a nuisance". This can include nuisance created by bonfires.
To be considered a nuisance the bonfire would have to be a regular problem and interfering substantially with your well-being, comfort or enjoyment of your property. Therefore if the fire is only occasional it is unlikely to be considered a nuisance. Similarly if you are troubled by a series of bonfires from various neighbours, each one of whom only burns occasionally, this will not be considered a nuisance because no single individual can be held responsible.
Approach your neighbour first to try and resolve the matter – they may not be aware of the problem they are causing and it may make them more considerate for future.
If this fails contact the environmental health department. They have power to take action under the Environmental Protection Act by issuing an abatement notice.
The Environmental Protection Act also allows you to take private action in the magistrates’ court.
Under the Highways (Amendment) Act 1986 anyone lighting a fire and allowing smoke to drift across the road faces a fine of up to £2000 if it endangers traffic. There may be local bye-laws which restrict the times which bonfires are allowed, however these are rare.
There are other methods of disposing of rubbish which are more beneficial to the environment: