Underpinning garden wall

[Zebra579]

Hi. I have had to lower external ground levels on my 18th century house, so that they are lower than internal ground levels. There is a narrow sideway where I have removed the concrete slab, but this leaves an adjacent garden wall with no foundations. It was sitting on top of the slab. The wall is about 2m high, 4" brick.
Clearly I need to underpin. How deep? How wide? Will I need to go around the neighbour's side?
Grateful for any tips.

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[^woody^]

Put a new 300mm wide and 150mm deep concrete strip 600mm lower than the lowest ground level, and then build up in brickwork