What is this and is it porous?

Try piercing holes in the plastic 1st to see if it helps any . If not it will need some sort if drainage installed.

Sounds like you needed a new soakaway installed if you have the space as there are regulations to but before doing that the builders May of wanted to do a percolation test to see if it drains, builders are great but I’d away a use a drainage expert when it comes to stuff like this. This is the work I do.

if the area is prone to holding water then a soak away should have been made. if it's clay then it should have been drained from the soak away also. The woven sheet sounds like a weed barrier and will retain water if the water can't get through it because of the clay underneath . would suggest removing and digging soak away and drain then replace the membrane then the shale should cure the problem.

Really need a picture however is there a slope away from the house so water is facing away yes put holes istal a bigger drainage repair guttering is ur brickwork water tight

Hard to say without seeing it but I would imagine that the blue material under the shingle is a weed proof fabric. I wouldn't go poking holes in it. Try pouring some water on to the fabric and see if it drains or sits on top. If it's not draining then some sort of soakaway would probably be needed.