Leaking conservatory roof problem

[D_Hailsham]

I have had this problem for many years. In 2007, about a year after I purchased the house, the roof was replaced (insurance claim) following storm damage. The problem only occurs in very heavy rain from the south. The flashing between roof and the house wall has been replaced several times but does not cure the problem. Internal damage to the house wall is now appearing. The suggested remedy is to replace the conservatory roof, but I can't see how that would cure the problem.

What's causing the water ingress and what's the solution?

Here are some pics.

 

[John D v2.0]

Sounds like normal water penetration not being dealt with properly after the installation of the should be a conservatory.
There should be a cavity
tray above the level of the flashing and weep vents from that onto the flashing.
The cavity is designed so water can fall down and drain out, as per the design intention of a cavity wall. If it is not draining somewhere appropriate it is a flaw in the wall.
If the wall above is fully rendered then there must be a defect with the render, but I'm assuming it's not.

The solution is to remove bricks above the flashing and add a cavity tray and vents, or render the wall.