My neighbors gas flue plumes directly into our garden.

[FiremanT]

Unfortunately, that couldn't be further from the truth...modern boilers do have much lower NOx levels but their CO levels can be extreme due to the modern burner design and minimal excess air they run with.
A correctly set up boiler will normally have low CO. ..less than 2 or 300 ppm but half a turn out on a gas valve adjustment is all it takes to produce CO ppms in the 1000s.
This is the downside of modern design, there is little margin for error...it's the consequence of reducing thermal NOx. Older balanced flue boilers were much safer with considerable excess air.

Commercial boilers push the combustion efficiencies even more and it's not uncommon to have CO ppms of 10,000+ from incorrect combustion.

If the flue terminal is over the boundary it's a non compliant installation.

GG: can you identify the boiler (and age) from the terminal?

 

[Gasguru]

The terminal appears to be from a condensing boiler....

 

[Chivas69]

Is that your back garden? Surely that flue is technically in your back garden!

 

[mattylad]

I see no reason why that flu could not have been taken through the roof tiles that are just above it.