Basement (External stairs) damp wall- failing bricks?

[roserly]

Hi,
I was hoping I could get an opinion to argue back with my landlord on the condition of my stairs. So any advice would be really appreciated! Excuse the lack of correct terminology. I am curently having major works done to remove damp and other issues in my property. We have these concrete stairs, which I was hoping would get replaced to metal stairs (to allow proper drainage and safe use)- as they are steep, uneven steps, slipperly and also adding to the damp. The wall adjoining the stairs is my bedroom, they are resolving the damp internally, they tanked the whole basement area, bar this bit of the wall and under the stairs. I got video shots of under the stairs- possible add a link to view if helpful. But here are some stills and a picture of the external stairs.
They advised they are going to remove the top layer (black bit) and resurface. That might make them non slipperly but not deal with the water penetration to the building (my bedroom wall)
The condition of UNDER the stairs, are the following
The pink area, the mortar between the bricks is like wet sand and chunks missing, some of the bricks look broken with chuncks missing.
The blue area under the stairs, the plaster/render? is blown and moisture is collecting behind there (i.e. my bedroom wall) its missing in areas as well.
The green area (under the stairs), sand colour material is water damaged and cracked and flaking away in layers, and one of steps has a deep crack.
The red area, I am sure is letting in water- I guess that would be addressed if they resurfaced the stairs.
The area just before the window and under the window- internally the window has signs of damp.
Their argument is that the damp can be stopped internally (whilst the wall continues to wear away from the outside?), it would cost £50k to replace the stairs (I understand more like £8-£12k) and the stairs has 20 years plus.
We have coal vaults under the paving, these were thankfully tanked with the rest of the basement area bar under the stairs. I know from the local authority as they had been inspecting all of them locally, that it can suddenly collapse, I dont suspect the stairs will suddently collapse, but the brick work which I am assuming is some what supporting the stairs looks terrible and the water penetration will continue, as well as the stairs generally beeing poorly designed to navigate down, especially with anything in your hands.
Any advice on condition of the stairs would be much appreciated- I was hoping to add the arguments, that removing the stairs will allow the damp/wall repair under the stairs and provide accessible stairs (i.e. structural or some other argument).