He came, he saw, He thinks it's the tree next-door.
I got him to be most thorough (says the man without a clue) as I really wanted it not to be the tree. He has moved the dish a little and it is much better, but I may have to look at what to do long-term.
It looks like I either need to get that tree trimmed or move the dish, which, technically, puts it on my upstairs neighbour's wall space. I've written them a note and if I get at least verbal agreement from them I may do that was opposed to risk anything with whoever lives next-door. i was nearly for going ahead there and then but, whilst he didn't say "I won't do it without their permission", he did seem most reluctant.
I live in a block of rented flats, but each flat just went to whichever landlord got there first. I spoke to the agency that cover my flat and they had nothing useful to say.