Dangling metal flue + air brick?

[PNE123]

Hello I am new to DIYnot. This week I had an old baxi bermuda taken out leaving a gaping old in the chimney breast. A new combi was then put into the kitchen. It was a big job and took 2 days.
Rather than just bricking the front of the hole up I am thinking of making a small cove using cement boards to put orniments in.
I have noticed that the metal flue has just been left and is just dangling and I can hear the pigeons! There is also some fibre glass round the outside of the flue. Can I just leave this in situ? Is it also a good idea to put an airbrick into the chimney breast?

 

[Elkato531]

Some photos would be useful. The fireplace opening can be boarded if you wish but it is advisable to keep it ventilated.

 

[FiremanT]

Who did the work, and what does your contract say. I have come across numerous jobs over the years where BG have specified and charged for removing the flue,but the contractors(?) have weasled out of it. Leaving me to charge for climbing the roof.