Very draughty working fireplace - help!!

[LG123]

We had a gas stove installed earlier this year. The previous owners had a gas fire but not a stove so the chimney was open.

We had a flue installed for the gas stove and there is a plate where the flue goes up into the chimney. From what I can see, the plate isn’t perfectly sealed in the space so there are some gaps where it’s not flush with the bricks. In this very cold last week we’ve noticed that there is a really big draught coming from the fireplace (almost like sitting by an open window)

My questions are:

• should the installer have sealed off the whole bottom of the chimney around the flue/liner? Or is it ok for there to be small gaps?
• Is there anything we can do further up the chimney/at the top to prevent the draught?

Any other help/advice would be massively appreciated as it’s currently unbearable to sit in the room and it’s making our whole downstairs much cooler…

Thanks in advance!!