Hi @Sebastian90
I think you all ready know the trick is to angle grind out the old soft mortar and replace it with more water proof mortar Admixtures. Older methods used to be a sand cement lime mixture the lime helps water to leach out. But mortar Admixtures or injecting the wall with waterproofing solution or drilling holes and inserting dryrods which react with water and seal the area is the more modern way. As well as the plastic water membrane you have.
The other question is where the water is coming from ? Wicking up from the ground? Or yesterday my neighbor showed me a hole in his roof and water was running down sarking in his roof to inside the wall lucky he also had planned weep hole open( no cement) mortar slots every 3rd brick to let the water out and air in when the roof is repaired soon.
You have two choices here the simplest option is as a DIY home owner option to simply refill the gaps in the mortar and make the wall look nice with an admixture water proof mortar may repel the acid effects of ground water and salts. There are also high strength structural mortars available at Bunnings But for a normal house standard mortar only needed. Just remember to match your mortar color and spritz the brick work wet with water as you add the new mortar to get it to bond to the bricks better.
Or a solution left more for a very advanced DIY person if the old mortar really badly crumbling dig it out and replace it the width of the brick you might use a large refillable caulking gun to pump the new water proof mortar deep into the brick wall easier than trying to trowel it in.
I would grind out the mortar 6 brick sections at a time at different locations around the house to speed things up using a large angle grinder and or a cheapie / old flat blade wood saw is good for raking out old mortar ( naterally if you ground a long continuous section of brick work the wall will want to collapse down wards. So do short sections at a time the wall should support itself.
Specialist companies drill holes in the wall and inject a sort of silicon based liquid that soaks into the brick work making it water proof. But in your wall the mortar looks like it could be replaced with a Admixture cement based mortar as the mortar its self looks crumbly?
