Passepartout

This is taken standing at the back wall of the house.

Hello, I'm a newbie here and I'd be grateful for some advice / wisdom. I recently relocated to a new home which has a small back garden 5mx5m, which is dominated by a Rowan Ash, slap bang in the centre. It's higher than the house and the trunk girth is about 900mm. The house was built in 1985 and so I think the size of the trunk suggests the tree was planted post house build. From the national geological survey it seems the predominant geology in this area is boulder clay (Till). Its a conservation area and I have obtained permission to remove the tree and a quote for the removal. I'm inclined to think that the risk of heave following removal of the tree is very low. Should I be more concerned about potential consequence of removal, should it involve 3rd party advice being sought and is it usual to inform the building insurer before removing a tree? Any advice will be gratefully received thanks.