Thanks for the offer, but my current client won't let me leave site and seeings she feeds me , although I do the cooking, and gives me a squeeze now and then I think it's a good job to be on.
Where do you see the water coming in exactly and when it did come in, was it both windy and raining or just that heavy, straight down, downpour stuff ?
Generally it doesn't travel that far sideways or up ways on a roof, as the little gullies between the slates help it keep a straight run down, unless your roof looks like The Atlantic on a blowy day. But yours does look pretty flat across it, until you get to about 500mm from the gable wall.
If you don't have felt, and I can't remember if you do, the water will fall onto the sarking boards and drip straight through the gaps. If the water is only running down the gable wall and nowhere else it's likely a chimney/coping issue like what Canardly said.
But if you didn't pay for any lead soakers or other flashing in your itemised invoice, you don't have any.
The original builder of the house would have saved a packet by not installing lead on all the roofs he built. If a builder wants to make a saving without the client finding out then the roof is where to do it, even though it's the most important part of the house as weather proofing goes.
I'm just wondering if the hat thing on the chimney has been left loose for the fire installers to fix for some reason.