The Mental Health Act in the UK and Australia and many other Countries acts against the International Convention of Human Rights.
I have used a highly unlikely question by to highlight the abuse of Government Power that can and does occur when the Mental Health Act is used to silence people.
It will all depend on your understanding of the word ‘object’ that you used in your question.
If you have a daily preoccupation with their smoke entering your airspace without your consent and you choose to voice those opinions daily and loudly then your objection might not make sense – with or without the fireplace.
Your neighbors have the opportunity by you voicing your opinion to actually remove you from society and pass all your goods and possessions over to the Government for them to manage.
This is what could happen.
Once they have contacted the Police and made several complaints the Police will immediately view you as a radical – you do have long hair. Your views on life which are not orthodox will be seen as placing you on the fringe of ‘acceptable behaviour’.
The Police wanting a nice shortcut to the whole episode will inform the local psychiatric unit that you are ‘ranting and raving’ in your backyard.
Not wanting to be injured and of course in need of some local content for their Phd’s the Unit Staff will obtain a court order to detain you for a mental assessment.
You of course know nothing about this nor the fact that the Mental Health Act judges you to be mentally unfit to interview and in need of detention.
They will arrive unannounced at your home. The Police will be there in numbers because by now you are judged to be almost a potential axe murderer.
If you do not open the door they will smash it open and enter with force.
You will object loudly. Ah that means you are deranged and dangerous.
They will taser you and then inject you with a sedative.
When you wake you will find yourself in a straitjacket in a padded cell.
You will be angry. Ah that is a sign of extreme violence. They will inject you again.
Then as you are still angry they will put electric shocks into your brain. At some point your Government appointed legal adviser will look at you and agree that you must be kept locked away for the rest of your life.
This is what legally exists at the moment in the UK and Australia and to the same degree in the USA.
My advice is to take up smoking.