Phone your local authority and ask to speak to a tree officer,arrange a site visit for an assessment of the tree and the issues you have with it.
Odiously trees need their leaves to live and produce oxygen etc, but with the right pruning regime, it may be possible (depending on species) to reduce this.
Some trees can have invasive roots that can damage foundations, if grown in close proximity to a building.
Trying to kill it yourself can lead to further problems, falling branches etc.
As I say, get in touch with your local tree officer, who should be able to give you a visual assessment and offer advice and also determine who has the responsibility and safety for the tree.