Phone the fire brigade. It might be different in England but I've put out bonfires where for example a gardener was burning branches in a residential area. We have a clean air act up here I think that means you're not allowed to have a bonfire unless it's supervised by a responsible person at bonfire night.
The officer in charge might use his discretion and tell them to reduce the size of it but chances are they will put it out for you.
Under the Environmental Protection Act 1990 (England, Scotland and Wales) a statutory nuisance can be any dust or effluvia from any trade or business premises or smoke, fumes or gases emitted from premises so as to be prejudicial to health or a nuisance. For a nuisance action to succeed the offence also has to be a cause of material harm or to be persistent or likely to recur. Nuisances may include smoke from bonfires, unpleasant odours, grit and dust. (In Northern Ireland statutory nuisances are currently regulated under the Public Health (Ireland) Act 1878, as amended, which includes powers for local authorities to serve abatement notices. The Clean Neighbourhoods and Environment Bill introduced into the NI Assembly in June 2010 makes provision for similar controls to those applying in the rest of the UK.)
In many cases a friendly approach to a neighbour or business can resolve the problem. If this fails, complaints should be made to your local environmental health department. If they are satisfied that a nuisance exists steps will be taken to abate the nuisance. This may involve serving a legal notice, which, if ignored, can result in proceedings in the Magistrates Court (Scotland – Sheriff Court). The Courts may impose an order to prevent the nuisance and a fine. Continued non-compliance can lead to further fines. The local authority also has power to abate the nuisance itself and recover costs.