Concerned about a neighbours tree in the hot weather

Anyone got any experience/ advice on trees in private gardens? There is a very large leylandii tree in a neighbour's garden. It's a rented property, always good tenants, however household and garden waste has accumulated over the years at the end of the garden and base of the tree. A lot of this waste looks very dry and combustible - wood, etc. The tree itself is also poorly managed with lots of dry/ dead sections and probably needs a good prune from a tree surgeon. I am concerned that the household waste and the tree could go up in flames in the hot weather with BBQs etc. I did seek advice from the tree officer at Haringey in the last few years, but was told it was a private issue.

This tree is so large that if it did go up in flames, it could affect several homes on our street. I am concerned for my own property and other residents, some of whom are vulnerable and could suffer as a consequence either tragically by fire spreading to their homes or financially if they don't have insurance, etc.

Any advice would be appreciated.