I am under pressure by my (very nice) neighbours to lop the top off our mimosa tree (acacia dealbata) which has grown strongly to about 30' high in a sheltered London garden and which is covered with yellow blooms from Feb to April. They a) would like more light (it shades about a 1/4 of their garden) and are worried it might take moisture out of the clay soil and cause heave/subsidence to their house (which is about 30 feet away). I am concerned that a major pruning would kill the tree or that it would be a flatter and wider shape after lopping and therefore increase the breadth of shade. Anyone agree?

dealbata seems to be rugged and could be pruned without risk of death. Start with cutting a few branches hard back this year, to show your neighbours that you care. The shape will change but there is no way round that. New growth from the cut branches will probably be more vigorous.
Their house is close in water terms so you need to act.

Starting another tree elsewhere would be a good idea. You could then remove the existing tree over a five year period, while the new one becomes established. Your neighbours would see steady progress towards more light and you would not lose all the lovely blossom at once.

very helpful replies - thank you!