A picture tells a thousand words! indeed.
Looking at your picture, I can't see much of an issue, regarding the operation of his boiler, the flue terminal still has plenty of space to breath and discharge and disperse fumes, and is not far from the front wall of your porch, (I am not disputing the safe minimum distances the flue pipe and terminal should be from the recommendations set by B.S. and gas safe practice) but that is as far as the safety is concerned, here I am talking about his boiler shutting down being blamed on your porch!
Nor is it too far from the roof line, his boiler is still working as you said, so where is the issue now with his boiler? like I said I can't see any issues that your extension/porch has caused to his boiler.
So this can be down to a few things :-
1. His boiler may have stopped, (if it at all did stop) due to another reason, and his gas engineer could not pin point the exact cause so he blames it on your porch being erected too near his flue or his flue being too near your porch.
2. Or your neighbour may have got concerned after you erected your porch too near his flue, despite you told him of your intentions, but after its erection, he realised how close it was to his flue, he calls a Gas safe engineer for his advise, and he is then told that your porch should not have been build too near his flue terminal,
or perhaps he may have told him correctly that his flue does not comply with latest safety requirements and should be moved, as it was installed in a wrong place to start with.
3. So may be the cheeky neighbor asks the engineer to state that his porch is too near his flue terminal and that it stopped his boiler from working, so he suggests that his flue should be moved to a safer location.
4. Your neighbour then hands you this report, in anticipation that you would take the responsibility for the cost of moving his flue to a safe location!
5. So now the bottom line issue is who really is responsible for this, and who should be forking the cost of moving his flue?
So in short the answer is him, he should, unfortunately he blames you because your porch erection cause this problem which was not there before, but you within your right erected that porch on your land, his flue should never have been placed there in the first place, so now the it is him who bears the responsibility to move his flue and the terminal at his cost.
6. You should now be able to enforce this on him through your building control to move his flue as it could be detrimental to the health and safety of your household as well as your building.
I can assure you his boiler simply did not stop because of your porch has been erected too near his terminal, it is not too near from operational point of view, but too close from safety point of view. His flue would have to be almost touching your wall before it becomes an issue to the correct operation of your boiler or it stops working as it cannot breath oxygen in!