Help with Boundary Wall - Its about to collapse into my property

Hi there,
I badly need help with a boundary wall issue. We live in a row of terraced houses. When the house was purchased the surveyor noted in his report that after inspecting the deeds and condition of the garden walls, that garden walls were needed attention and that we should look into rebuilding/repairing.
There is then a picture shown, showing the right hand garden wall, with my back to the house. In chatting to the neighbour/landlord he also believes that this wall belongs to us.
With this in mind I spent most of last summer repointing this wall, and cementing the capping stones.
The boundary walls either side of us are a single skin red brick wall, 1 metre high, with supporting pillars every 4-5 foot. There is no rear access to any properties in our row of terraced houses as there is either a 12ft high wall or gable end wall of another house.
With our wall safe and sound I looked at trying to get the neighbour to re-point theirs on the left hand side (again with back to wall).
Unfortunately this isn’t simple as the house is rented out, and all contact MUST go through the letting agent. They have “allegedly” spoken to the landlord several times who claims the wall is:
• Either not there wall so don’t want to know.
• Claims it’s a party wall so only willing to do anything if we pay half
• Claim the wall only needs repointing and would be £900, so £450 each.
This may have been the case when I started chasing this 3 years ago, as each year has gone by the frost cracking has become worse and the wall is BADLY leaning into our property.
I have purchased the maps & info from the land registry costing £10, and sadly just shows maps, and pointless text with nothing clearly marked.
We have 2 young girls who last year couldn’t even play in their own garden/Wendy house as it is too dangerous for them to be in the garden.
With my little finger I can physically move the entire length of the wall and I am fearful it could now collapse at any minute. There are already 4 bricks that have come out of the wall and are on my property.
I have yearly chased the Letting agent with the same rubbish responses every year.
My objections on paying for the wall to be repaired are the following:
• I do not believe it’s my wall. The wall I am responsible for I have repaired!
• The wall is actually being use as a soil retaining wall, by said neighbour. As several extensions have been built over the years, rather than extract the soil through the house, which is the only option, they have illegally with no planning permission, raised the original ground level.
I can happily prove original ground level, through the roof pitch of the house, the original quarry tiles for what was the yard, and 1 inch below my top soil and are very obviously as it would have been, a quarry tiled yard.
The soil/increase in ground level is the sole reason why this wall is about to collapse, the wall was never designed as a retaining wall for soil, and when it rains, water comes through the wall with dirt and mud from the soil of next door.
The soil slopes from the middle of the garden and raises up to over 93cm up the wall. The soil is also 93cm high against the gable end wall of a house, easily breaching damp proof and causing damage, sadly this house is also rented and struggle to find landlord to so if we could both attempt to fix the issue together.
However because no 1 knew the ground level had been illegally raise and because it has been this way for more than 3 years, the council have advised it automatically has planning permission.
• If it wasn’t for this soil, I would just bite the bullet, demolish the wall and put 6ft panels in, and have a much better and more private garden. However as soon as the wall is demolished large amounts of soil will land in my garden.

I have spoken to the local council from a H&S point of view and the environmental health team said they would be interested in helping, but the help with be on the way of slapping an order on both properties, taking the whole thing to court IF no 1 acted, and then it would be down to structural surveys and planning people to argue the case, but would all become expensive.
I just really need a sensible solution to this so we can enjoy our garden, and the kids can play in the safety of the garden.

Any help/advise or solutions would be amazing, as I have now just resigned myself to the wall falling down and then trying to deal with and claim damages to my shed, patio etc.