Paul, apologies for not replying, I've not been on Arbtalk a lot recently.
I'm no expert on this compensation business, but some basic principles would apply. As said before the tree would have to be TPO'd. And then there would have to be an application for its removal, citing damage so that the case can be made afterwards for foreseeable damage. So one could say that although the wall is leaning, its salvageable but if nothing esle is done it will fall over because of the tree. The measure of damage would start with the cost of rebuilding the wall. It might be safe to say it's slightly more expensive to rebuild to accommodate the tree (say, with a ground beam).
It woudl just be a matter of dispute threafter how much of the cost would be payable in damage. Negotiations would take place in the shadow of a Lands Tribunal application by either party. So the approach to valuation should be adopted that the Tribunal would use. Past experience tells me they don't just find in favour of one party of the other, it's more likely to be a partial award. The Tribunal seems to be persuaded more by actual costs incurred than by estimates, becuase it shows genuine intent to reinstate the wall and it removes cost-uncertainty. After all. getting £6k to rebuild a brick wall then spending £1k on a fence instead is not 'equivalence'.
I'd say it's a matter of degree, then, a % of rebuild costs, based on how much damage was already done before the compensation application (not compensatable) and how much afterwards.
It shouldn't be necessary to wait for the wall to fall over if someone with an engineering background could certify that its removal was necessary because of foreseeable harm.
My only big case in Tribunal, for a Coucil I offered £50k and the claimant wanted £125k. The Tribunal awarded £69k but because of procedural errors on the Council's part the claimant was awarded costs too (of £9k mainly legal fees). It's a typical Tribunal horse deal with no certainty on either side.
So in conclusion I don't think the extra rebuild cost is a factor, it would jut be a higher figure for the % apportionment to be based on.