Certainly an ash tree shouldn't be 1m from the extension on clay. I would get the insurance co involved, but you might also, if you have legal expenses insurance with your house, have a chat to them about the tree and potential issues and see what they say. It may be a long road, and the tree may have a TPO, but ideally the tree should probably be removed. However, there is the caveat that removing a tree can cause "heave" - the opposite of subsidence. You may well need input from a tree expert.
Don't rush - take it a step at a time - do you get on with the neighbours? how close is the tree to their house? Big trees - ash, oak, lime, sycamore etc really should not be very close to buildings. It would be better to solve the problem through cooperation and dialogue, but if that isn't possible, potentially it could go legal.