The subject of bonfires is quite simple really, but seems to be clouded in myth and misunderstanding.
There is no such thing as ‘common law’ in respect of bonfires. It is a common misconception that there are bye laws to prohibit bonfires, or limits to the time of day when they can take place. An outright ban would be difficult to enforce and often a bonfire is the best practicable way to dispose of garden waste. An occasional bonfire should not cause a problem so long as it does not affect any neighbouring properties.
Basically, if you want to light a bonfire to burn rubbish you are free to do so, subject to very few restrictions.
If you have regular fires then that could be deemed to be a nuisance and, if a neighbour complains, the local council must investigate and can issue a nuisance abatement notice under the Environment Protect Act of 1990.
Under the Highways Act 1980 anyone lighting a fire and allowing smoke to drift across a road faces a fine if it endangers people or traffic. There is no reference in the legislation to any distance of a fire from a carriageway.
This is a police matter, not for the local council.
The law says: (1) If a person --
(a) Lights a fire on any land not forming part of a highway which consists of or comprises a carriageway ... and in consequence a user of any highway which consists of or comprises a carriageway is injured, interrupted or endangered by, or by smoke from, that fire or any other fire caused by that fire, that person is guilty of an offence and liable to a fine not exceeding level 5 on the standard scale.
(2) In any proceedings for an offence under this section it shall be a defence for the accused to prove that --
(a) that at the time the fire was lit he was satisfied on reasonable grounds that it was unlikely that users of any highway consisting of or comprising a carriageway would be injured, interrupted or endangered by, or by smoke from, that fire or any other fire caused by that fire; and
(b) either --
(i) that both before and after the fire was lit he did all he reasonably could to prevent users of any such highway from being so injured, interrupted or endangered; or
(ii) that he had a reasonable excuse for not doing so.
However, on an allotment site, although the law must still be obeyed, the regulators of the site (Local council or committee) are free to make and enforce any additional regulations they wish.
If they say ‘No Fires’ then that’s it. No fires.
If they impose time restrictions then there are time restrictions.
That's it. It is their duty to make and enforce rules for the benefit of site users and others.