joining conservatory to stone wall

[MaxB]

We have just had a conservatory fitted, (at great expense) but each time it rains, water has leaked down the inside newly plastered wall and appeared to be from behind the box guttering. (hip back glass roof to house wall)
It appears the firm have just stuck their lead flashing, under our old lead which had been above our derelict back porch we took down. They came out again last week, and the site manager went up and stuck a lead piece over the split in the old lead, which got me thinking the worst.
I have been up to look this morning and taken pics which made my heart sink.

They have not chiseled out a groove from the stone, to insert the new flashing, which is surely the only way to prevent water ingress at such a crucial joint?

 

[catlad]

I have tried clicking on the image tab but nothing happens?

 

[MaxB]

Hope pic has come through now, from all I've read, the new lead should have been deep set into channel in the stone

 

[catlad]

Were does the water show in the house?

 

[MaxB]

It seeps down behind the structure and straight down the newly plastered wall. (they first tried to tell us it was condensation!)
And here's what they plaster boarded over