Party wall water penetration

I am in the process of undertaking a loft conversion and as part of this I extended the existing party wall. However, water is penetrating through from the neighbours side and I am after advice as to the best way to tackle it.
I have attached a photo showing part of the wall internally.
The darker bricks are original and were the upper course of the party wall.
Under these bricks is a DPC and there was also lead flashing which is still present on the neighbours side.
Whilst I thought at first that the water may be penetrating through on top of the DPC, I now believe that the bricks themselves are getting soaked (possibly because the mortar holding in the lead flashing is defective) and this is how the water is getting through.
With hindsight, I realise that I should have cut a gap into the top course of the original brickwork to prevent water passage but at the time this didn't occur to me.
From my new flat roof, with a long pole I can reach the offending brickwork on the neighbours side and may be able to apply a sealer but there is not really anything else I can do on their side.
I can obviously apply a sealer on my side but I don't think that is the best solution. Another thought I had was to install some form or drip tray on my side so that any water that does get through (it's drops rather than a torrent) can be channelled away somewhere.
Any ideas would be welcome.

Sorry, I can't get my head around this. Is the brickwork above the soldier course half brick thick (non bricklayers call it single brick) or does it have a cavity?

Just that, the outer leaf of a cavity wall doesn't necessarily keep water out, hence weeps on wall ties and cavity trays.

If it's a 9" wall it will get wet on the inside.

An external image or drawing of what's actually been built would be more useful

Bonni,
Yes, the brickwork above the soldier course does have a cavity. So I guess what could be happening then is that water may be penetrating the outer wall above the soldier course and this water is then collecting on top of that course which is why the bricks are so wet.

Woody,
I don't have any images that show the completed roof but have attached one that shows the roof under construction with the party wall on the left.

There should be a cavity tray built into that wall.

It seems to me that now, all that will happen is water will enter the leafs and run downwards until it reaches the brick on edge.