Firstly, I'm not doubting your statement that the wire is rubbing on the tree branches, especially when windy. But from an engineering perspective, it would have to be proven so before renewal of the wire is undertaken. The actual fault could be in an underground joint 2 miles down the road, for example.
From what you say though our test equipment should easily identify the issue, and usually giving the wire a good whacking with our 'height measuring rods' can generally simulate the windy conditions, thus enhancing the fault condition for detection purposes.
If it is proven to be the wire, there are various options open to us ............ including feeding from a different DP as a last resort. The usual course of action would be to prune the tree, if it's light foliage we are obliged to attempt it ourselves, but looking at your picture I would probably have it farmed out to a local contractor.
We also have a specific wire designed for this situation, that has thicker insulation.
If 're-feeding' from the other DP (Pole) is to be utilised, then it's simply a case of asking the neighbours permission to 'bounce' the wire onto and across their properties. If permission was given, a far neater job would be for the engineer to use CAD55 wire from the pole to the gable-end premises. This is a multi-core cable that would carry all 3 circuits in the one wire, rather than have three separate wires 'flying' from the pole to the premises. A BT66 connector block would then be fixed and all three circuits run separately from here, to each individual premises.