Corbelled foundations on party wall very shallow - any solutions

[nmh]

Neighbours and I make up a Victorian semi build @ 1895 in SE London. They've recently renovated theirs and extended kitchen/living area into the garden. Their builder poured a 200mm concrete slab with 8mm mesh top and bottom into the excavated space (see picture).

 

We're now doing the same kitchen/living area extension (see side elevation drawing) but on digging inspection hole at the internal party wall can see how woefully under specced the existing corbelled foundations are (see picture). Apparently concrete pours on top of London clay can be an issue.

 

We want to create/maintain good ceiling height in the new kitchen living area and wondered if anyone had success when foundations this bad. Obvs architect and structural engineer involved but wondered if anyone had successfully overcome something similar. 

 

Many thanks.