If I was in your position I would replant the slope with some relatively deep rooting shrubs. The roots will do a much better job of tying it all together than your retaining wall will of holding it back - after all it worked for the previous 27 years.
Looking at the topsoil I suspect that your subsoil is heavy clay, and given that are in Rotheram it's a fair chance that it is weathered coal measures mudstone. I suspect that the slope will stand for a while but not be stable in the long term at that angle as you have removed the plants whose roots physically tie the soils together, and who also act to remove water from the slope effectively increasing the shear strength of the clay and making slope failure less likely.
You can get an idea for what angle the slope would stand at above the wall by looking at natural slopes in your area - these will be at the long term angle of stability for the local geology. For clays this is typically a around a maximum of 1 in 3 depending on the plasticity of the clays. Of course you need to make sure that you aren't looking at a sand/sandstone or mudstone slope which are also common in your area. Your slope almost certainly isn't natural and I suspect that is has been over-steepened by removing the toe to form the lawn area.
Low permeability over consolidated clays will stand vertically in the very short term, and still at steep angles in to the medium term due to the negative pore pressures induced by cutting the slope, but over time as water ingress occurs, those negative pore pressures dissipate and with it much of the apparent strength of the clay. Your slope may still be loosing strength and becoming less stable as it moves to a new equilibrium moisture content following the removal of the shrubs - this can take years in very low permeability clays, but if the clay is even slightly sandy it could be much quicker and may have happened already.
Of course if your slope is actually sand or rock beneath the topsoil then all bets are off and it could be stable as it is, and all you are seeing is mobilisation of the topsoil in the near surface due to the lack of roots, loss of soil structure from being dug over, and lack of protection from the rain from the loss of trees. Either way, planting probably isn't a bad idea.
Looking at the topsoil I suspect that your subsoil is heavy clay, and given that are in Rotheram it's a fair chance that it is weathered coal measures mudstone. I suspect that the slope will stand for a while but not be stable in the long term at that angle as you have removed the plants whose roots physically tie the soils together, and who also act to remove water from the slope effectively increasing the shear strength of the clay and making slope failure less likely.
You can get an idea for what angle the slope would stand at above the wall by looking at natural slopes in your area - these will be at the long term angle of stability for the local geology. For clays this is typically a around a maximum of 1 in 3 depending on the plasticity of the clays. Of course you need to make sure that you aren't looking at a sand/sandstone or mudstone slope which are also common in your area. Your slope almost certainly isn't natural and I suspect that is has been over-steepened by removing the toe to form the lawn area.
Low permeability over consolidated clays will stand vertically in the very short term, and still at steep angles in to the medium term due to the negative pore pressures induced by cutting the slope, but over time as water ingress occurs, those negative pore pressures dissipate and with it much of the apparent strength of the clay. Your slope may still be loosing strength and becoming less stable as it moves to a new equilibrium moisture content following the removal of the shrubs - this can take years in very low permeability clays, but if the clay is even slightly sandy it could be much quicker and may have happened already.
Of course if your slope is actually sand or rock beneath the topsoil then all bets are off and it could be stable as it is, and all you are seeing is mobilisation of the topsoil in the near surface due to the lack of roots, loss of soil structure from being dug over, and lack of protection from the rain from the loss of trees. Either way, planting probably isn't a bad idea.