Having had the same problem as the above since I used Sonax. I have today cleared the system. I removed the offside wheel liner and water bottle. You only need to remove the rear half of the liner.
The filters were covered in a yellow "ish" sludge. The sludge had a lemon smell just like the Sonax I used when the problem started. I have already taken the vinegar route plus pumped water in all directions but obviously nothing had move it.
Here you can see the water bottle.
Here you can see the front pump just lifted from the bottle with the sludge strung out!
Here you can see the rear filter on the black pump coverd in the sludge. The rear jet was working but not too well. The front jets were useless.
Both pumps are the same level and work from the same reservoir. It will just depend which one is blocked. I imagine the fronts block as they are used more.
So now I have perfect washers all round having cleaned this mess out

. I did not have this problem until I used Sonax so in my case I blame that. It happend pretty quickly but I believe it could be a gradual problem in some cases. The water bottle was drained when I put Sonax in so I do not believe it mixed with the BMW wash to create the blockage. I am now using BMW wash again, not because I believe it is the best around but at least I know it works.
I reckon you could put something in the bottle to disolve the sludge as the pumps sit right at the bottom. For me vinegar did not work but perhaps Cillit may have done. You will just have to be careful and flush it all out.
At least you can see what you are dealing with now.
If anyone has a go, you do need to remove the indicator on the wing as it's wire is fastened to the water bottle and needs to be free. You push the indicator forward to compress a small spring and pull it out at the rear. It may be a stuck in place at first.
Edit
Just to add, if you carry out this procedure, some thread lock liquid is required for the one bolt that secures the water bottle in place when refitting. Regular strength liquid is fine for this.