Drill holes in the stump and pour in SBK Brushwood killer.

It will take years & years to break down and those chemicals are caustic. I would hire somebody with the equipment & technique to make it gone in a day without harming the ecosystem. They aren't unreasonable.

is the root under the building?
I too would go for SBK, if you can saw off as much as you can then pour /paint the cut surface. cover with an old bucket/polythene to stop it getting washed off. This will prevent damage to the soil and when dead fungus will move in and rot the stump away.

or ask a professional tree surgeon/arborist to grind it out. May be a problem due the building behind it though.

The 'tree surgeon' would remove the main stump and surface roots so that you can reuse that area for something else. Any roots left underneath are dead and will quickly decompose. No need to worry about that.

Cheers guys!! Might just try the Brushwood😉

welcome to GoY by the way. forgot to welcome you when i replied first time.