Water ingress possibly from gap under bungalow roof tile

[Gregzilla75]

My bungalow has a water ingress problem from before I moved in and the corner ceiling of a spare bedroom keeps getting black. I plastered over it after removing some loose bits and painted it with sealant but the black mould has returned. Looking at the external area where this is coming from it seems an attempt has been made to block it up with some orange foam (?) and as you can see in the pictures there's a cracked/loose piece of concrete at the side which I'm guessing is the main cause of the problem.

Would you suggest this is an easy DIY fix or should I call in an expert? My DIY competency is very low!

I'm thinking pull that piece of concrete out and reset it with some new material and reinforce the orange parts with some more of the same material (whatever that is).

Any guidance would be much appreciated. TIA.

EDIT: I've just been up into the attic and as you can see from the photo there looks to be a mass of some polystyrene type filler, I guess. Is this normal or is it another sign of an attempt to stop damp getting through? The insulation is also black and filthy, once the ingress problem is sorted I will set out replacing the insulation and eventually gets some basic flooring down so the attic can be used for storage.

 

[Wayners]

Lift tiles and see if water has been running down the felt. You will see evidence of this on felt plus tile batten will be rotten.
The felt should drop in the gutter but probably rotted off from sun over the years so water is falling short of gutter, then running inside house.
Fit felt support along there.
Fit new batten.
Mortar up the end tiles.
Then trace where water is getting under tiles and fix. Could be further up roof so follow the evidence you will see on the felt