You would have to check with your local council but most authorities don't have any rules, laws or regulations regarding bonfires.
However, if this a continual thing, there is a nuisence law which can be applied. I presume your local bobby (if you have one) can advise you. I'm pretty certain no action would be taken if it was just one-off.
Meanwhile, take photographs of any smoke, soot or other damage and and keep a written log. You could also try talking to your neighbour and tell them of your concerns.
We have someone up the road who does the same....usually just as we've put the washing out and getting ready to have dinner in the garden on a nice summers evening !!!
Good luck