HA want to remove cherry tree from our front garden :(

I doubt that there is any way to fight it and although it's not what you want to hear; I suspect that removal of the tree is in everyone's best interests.
Trees are not removed without serious consideration.

Most trees continue to grow until they die. It is likely that your cherry is still growing, but perhaps only six to twelve inches per year, so that you hardly notice.
Cherry tree roots are very large and notorious for lifting up pathways, damaging foundations, causing subsidence or breaking underground gas and water pipes. The general guideline for cherries is that the roots will be about twice the size of what you see above ground, which is why they can be so destructive. These roots gradually thicken each year (like a tree trunk gets thicker as the tree gets older) and the thickening can cause ground heave.

When the tree is gone, plant another tree with smaller roots, such as an apple. Apple roots only spread about the same as the above-ground part of the tree. I dare say that if the tree in your garden was an apple of the same size, it would not be on the removal list.

You could try getting an independent expert to report on whether it's causing damage/has potential to cause damage and then forward that to them to back up your case if he doesn't agree.

Otherwise look on it as an opportunity, perhaps you could plant a dwarf apple or edible cherry as a replacement.

Sadly I don't think it's even as informed as you say FB - the guy did not know it was a cherry tree until I said, he simply wants it down because it's a tree and it's close to the house. If it had been an apple tree, any kind of tree, it would have been the same. They are not going to remove it in it's entirety, they are going to cut it off at the roots, then drill into the stump and put root killer into it. So it's not even like I will be able to plant something else in it's wake because there will be a big poisoned stump there.

Can anyone tell me if they do take it away and kill the roots, will the root killer affect other trees and plants around it? There is a plum tree 'twig' at the base of it, I could save that by pruning it back enough that it wouldn't be hurt by the cherry tree being felled, but would the root killer stuff spread? If it did, it would kill the plum too.

Well, it's the sad judgement day for the tree, I decided to let them take it down as they have agreed not to touch the plum tree and not to put root poison down, only take the cherry tree down. Boo hoo! A man is outside planning its untimely death as I type!