I agree.
I bought a house that was cracking and I insisted that the vendor initiated a subsidence claim on his policy prior to them moving out. The first thing the insurers did was to appoint their loss adjusters who immediately carried out soil tests, which identified roots of nearby trees belonging to the council. They then wrote to them pretty much as Mr_Numbers has put it here and I guess their professional weight, as opposed to little ol' me, did the trick with the council's tree officer taking rapid action against the offending trees.