I find the Garden Law website a particularly fruitful (no pun intended) source of information in this area.
Look here under trees - and the bottom of the section about roots.
http://www.gardenlaw.co.uk/trees.html
I am not 100% sure, but I suspect that the situation about roots growing under a boundary and causing damage is a parallel example to your situation about wall climbing plants doing the same above ground.
If that is true, you are not permitted to legally go over to cut it back without permission, however you could be sued for damages under the 'nuisance' legislation.
As always it is best to try and get an amicable solution to this - by talking to neighbour and offering to cut down before it causes them an issue.
If you don't get a better answer from AB, you could ask your own question on the garden law forum.