Tree on your property, you open and are responsible for keeping it safe and for any damage to (eg subsidence) it causes, that’s the law. Legally though there is no way to force removal….if there were I’d be using it to get trees out from neighbours. Yes trees are nice, but in the right setting. A large tree in a small urban garden, close to buildings is not the right setting. Depending on soil type, that tree is easily big enough and close enough to the buildings to cause significant damage through subsidence…..I hope it’s not clay soil.
It’s a syc…. It’s nice enough but **** me, it’s just a syc. They are weeds, not a rare elm, majestic oak or beach or such.
Your neighbours are being exceptionally nice to ask nicely and part fund.
If you have a wood burner syc is ok, I’ve had loads and loads and my experience is it’s about the most reliable easy splitting wood, it dries readily but for a hard wood it is not that dense. It’s worthwhile, but not incredible… Density at 20%mc is about 0.55-0.6 which is comparable to Leylandii (which is actually very dense for a softwood). Get the tree surgeon to chip everything below ~4″ thick and to ring the trunk up (they almost certainly will ring it to bring it down anyway, except the last 15 feet, but would ring that to be able to carry it to the street). A mature syc….3-5 cube of firewood probably.
Stump, if you need it out and there is access to bring a grinder in then get it done for you. Otherwise, just accept it and stick some pots on it or if feeling fancy get the last 8 foot of trunk left and a carving done. The stump should be easily killed with glyphosate/rosate, the tree surgeon should groove out the cambium and apply this. It might need another application next spring.
My experience on large trees, removal from similar garden, a grand cost to fell and remove but not grind the stump.