Sorry about that, I didn't catch that the whole foundation was thought to be this early agg/lime mix... I have seen thin base layers (failing similarly to your's) of say 150 to 300 cement-like material below a spread brick foundation. These are notoriously (in my own mind) difficult to remediate as the underpinning suggested by Dik and alluded to by BAretired nearly always results in brick falls.
I agree with our estimed colleagues; You are most likely going to have to replace this foundation. I've provided new foundations adjacent to existing (insufficient, failing, etc) foundations, needled the wall above and carried the existing wall in this manner. It is difficult, expensive, and requires access to both sides. Otherwise you can repair/remediate the wall by needling the existing onto temporary founds (again, normally requiring two sides of access) and remove/replace/repair the existing foundation in-situ.
Now just in case I'll point out that Needling is the process of removing some bricks (often in multi-whythe walls) and passing a beam perpendicularly through the hole to carry the bricks above while you work on/replace/remove the bricks below.
Okay, so there is still yet another possible solution: Replace the existing load carrying system with a new wall and foundation; This is not cheap, but is sometimes quite practical... I've seen this done (in a magazine), though never attempted it myself. Essentially you are being wholly unsympathetic to the existing (and possibly historic) structure, but it is on occasion the right way to go as it can permit full change of use/expansion/replacement of the structure.
Good luck and let us know how it goes,
Cheers,
YS
B.Eng (Carleton), P.Eng (Ontario), MIPENZ (Structural-New Zealand)
Working in Canada, and missing my adoptive New Zealand family... at least I brought the little Kiwi with me!