Taking them to court would be by judicial review, unless you have £20k plus to waste you won’t even get through the door of the high court.
As fatgit says the way to take it forward would be through the council complaint then ombudsman route. This can only be for how they investigate, if they have investigated and said not a nuisance then there is probably nothing you can do.
How often are the bonfires? Daily, weekly, monthly, yearly? The threshold for a stat nuisance is fairly high, it has to be more than an annoyance.
You can take your own private action under Section 82 of the EPA 1990, that cuts out the council all together and you go straight to the magistrates court.