Lighting a garden bonfire is not illegal – it is the smoke that can be a statutory nuisance.
Your local council environmental health departments can take action if the smoke from the bonfire is classed as a statutory nuisance.
Please contact them for further details as below
Barnsley 01226 773555
Rotherham 01709 381212
Doncaster 01302 736000
Sheffield 0114 2734567