I fear there may be a lack of middle ground on this one. Note, this is very much a non-expert perspective, but as a homeowner dealing with equivalent issues.
Assuming the installation was made pre-2010, or can't be proved to have been made later, then it pre-dates Part J of the building regulations so anyone could do it. That also means there were no restrictions on the type of appliance installed (no emissions standards to be met). My experience with an oil-fired Rayburn (I grew up with one and Mum still has it) is that they burn with an oily smell when they are set very low, ie over summer. If it is on because it is his source of hot water/cooking then he may not have many other options, at least cost-effective ones. Building regulations, like automotive regulations, are generally not retrospective, so unless it was non-compliant when it went in, or has become so against a specification it should have met at the time, then there isn't much that can be done to force someone to make a change. The only 'global' changes which affect this are designation of zones, e.g. smokeless.
There are some activities which would qualify as a nuisance, which would be what an environmental officer would assess, however my experience has been that this is down to their opinion more than any hard and fast rules - like much of English law, they form a view, they express it, if you don't agree then you can test it by not following their instruction and they can then test it in court. I had a conversation with a council planning officer last year (all very polite) in which we established that nobody knew how deep you have to dig for it to constitute 'excavation' (I had temporarily stripped back some topsoil about 8" deep) and we both concluded that it really wasn't worth either of our while to go to court, so long as it went back in a few weeks (which it did). Some officers are very draconian in their view (I used to live next door to a village hall where the annual village fete was held on a Sunday afternoon - the last year it ran, everybody was greeted at the entrance by an organiser asking them to please talk quietly, there was no music and announcements were not made, due to a letter from the environmental officer following a pre-emptive letter of complaint from the house the other side, owned by a man who had previously complained to the council about the noise of children queuing up to go into the building in the mornings when the hall was still the village school!) However, I would urge caution in getting the environmental officer involved unless you yourself choose to live invisibly. The problem is that if you find you do have a draconian one, it may result in a letter to your neighbour, but is then equally open to setting up a tit-for-tat exchange over anything of yours he may not like (mowing the grass at a time he finds inconvenient, working in the shed/garage at a time he doesn't like, old land rovers around as a visual eyesore etc) and if the officer backs one he may well back another. There is then the point of what happens if a letter is sent and ignored - if the council doesn't pursue it then all you have is a worse relationship with your neighbour.
When you mention it, what does he actually say? If he doesn't know what to do about it then his options are limited. Have you waited until a still day when it's particularly strong and then asked him to come round and experience it for himself? It's much easier I find to get admission that something is a problem when it is staring someone in the face (I manoevred the listed buildings officer into the area of a room where the ceiling height had been reduced to 5'3" and had him standing there while I explained that removing the inserted ceiling might make it easier to use the room - very difficult to disagree while his neck gradually developed a crick from standing there!) You might also need to do the research to track down possible root causes and solutions - the emissions do clean up with a regular service including a wick change so if while standing 'experiencing' the fumes he agrees that maybe a service would be a good idea there is no harm in having a name to hand of someone who could help if when you ask if he has a regular service engineer he admits that he doesn't. It also lets you remind him in future with the question 'have you rung XXX yet?'
Alec
