John Wilson wrote:
There is a large tree outside my house

It's not on my land but it causes problems on my land.. gutters/mess/wasps.

So whose land *is* it on? Neighbour? Council?

It's at least 40 feet tall

What is my options to get rid of it

For starters, have a chat to the trees owners and sound them out as to
what they think about it?

David