Is this chimney flue connection correct?

[Dario]

I found that the gas fireplace chimney crown on my house was pretty cracked and allowed little water in.

After removing the crown I discovered that the flue was fitted hovering two inches above the concrete chimney pipe end and not interfaced to it, potentially allowing fumes to go into the chimney box - I did find soot deposits there. Furthermore, there is flexible flue liner running inside the concrete pipe but it stops about 30cm below the top.

 

Couple of questions now:

1. Isn't the flue supposed to be tightly connected to the system below without the break gap?

2. If so, can it be interfaced and sealed to the concrete pipe as the lining ends 30cm too low or will I have to replace the lining with a length reaching all the way to the flue?

 

Please see the photos.
The chimney itself is precast concrete on a metal frame. Note the heat boards are removed in the photo as I am going to recoat the frame.

 

Many thanks for any advice.

 

Chimney in loft with heat boards removed

Starting on the crown

Pretty rotten underneath and the reinforced concrete top also crumbling

Flue was flat on top of the rusted plate with a 2" air gap under it

Flue liner down the concrete pipe