Oh dear. Yes, I've seen this sort of thing a few times.
Whenever works involve Building Control (local council), there are very keen to see that there is no detriment to neighbouring properties. Of course, here, the bad guys have been and gone.
I would imagine you have a good case in Law, but, a long and upsetting scenario for all concerned if you did get solicitors involved.
Being pragmatic, I would be prepared to do some remedial work yourself. Permission from the neighbours should be academic, as they are technically at fault.
A simple solution is to dig a small trench the length of your building. The depth only needs to be to a little below the original level... below the airbricks, and approx 6" (150mm) below the dampcourse as a minimum.
The width of this trench need only be 150mm (6"). A neat cut with a disc cutter would give a nice edge, but not terribly durable. Better, would be to widen the trench to 9" and fit concrete edging kerbs. They're only a couple of inches thick.
If clean chippings are laid in the bottom of the trench, then this will drain water to the ends, where this water can be led to a very simple soakaway or surface water drains.
This is necessarily only a brief description of the work, but you should get the picture.
For a decent builder/handyman, it really is a very simple operation... not as scary as it sounds.
An alternative to kerbs would be to use linear drainage grids ......... I'm sure you've seen them.......... about 3' long by 4"..... metal with slots in them.
The idea is to expose the airbricks and the lower brickwork to the air to keep it "breathing"