Help, rain is penetrating my conservatory wall

[Suzcooke]

As it's so shallow could I just fill it with mortar and slope it away from the wall that so any water runs into the patio?
Snatching at straws here as I have no idea what's best for the long run

 

[Doggit]

Does the trench go anywhere that would take the water away; or can you carry it round to a drain. It's possible that they've tried to create a drain system, but then filled it with the wrong type of stones. Try digging all of the gravel out, and then see if the problem goes away.

 

[Suzcooke]

Hopefully you can see from the pic that there seems to be nowhere for the water to run

 

[JohnD]

I have a feeling that the new slabs were laid on old concrete, and the gravel gap is just an ornament. Or a moat.

I would be thinking about creating a groove to let water run out of the trough.

 

[Doggit]

Does the channel go round the corner though.

 

[John D v2.0]

I don't think building it up with more mortar is the ideal solution, just in case it can't dry out any more.
Do the flag stones slope towards the channel? If you put water in the channel does it go anywhere (other then inside)
If it doesn't have anywhere to drain at the moment, you could lift a slab and put a pipe in to take the water away somewhere lower.
But the long term solution would be to reduce the ground level, as above, it's common for new patios to be built on top of old, until eventually it's too high.
A third solution if lowering is impossible, would be to get down to the dpc, chase a damp proof flashing in just below, and run it up the outside of the wall to above ground level.
If you visit the site pavingexpert, they have the gold standards for paving and levels. We did our drive using that information and it's turned out brilliantly.