Advice on neighbours tree please

2 doors down is a very large leylandii tree, in the rear garden.  Household and garden waste has accumulated over the years at the end of the garden and base of the tree, possibly from previous tenants. 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 however immediately 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 so I have come to a dead end on this.  I have also sent this to a local councillor.

This tree is so large that if it did go up in flames, it would affect several homes on our street.  We have vulnerable residents, one of whom lives next door and could suffer as a consequence either tragically by fire spreading to their homes or financially if they don't have insurance, etc. 

The best scenario would be to contact the landlord of the property but don't have details of this. Any ideas?