First thing to do is check whether you are in a smokeless zone or not 🙄
There are many types of chimney pot, depends on weather, updraught and stuff like that, go to a local builders merchant for advice.
You may need to get your chimney/fireplace re-lined if it has not been used for years, may be the reason your house filled up with smoke = loose/missing mortar ===== Biggest cause of house fires, people openingup old fireplaces/chimneys 👿
Please say yes or no with basic explanation.
I am no expert, just depends on how much you value your house/life etc 😈
An example;
Yrs ago whilst playing squash in an old converted church with adjoining houses we had to stop due to the court/building filling up with smoke. We could not find any signs of fire except for the neighbours chimney having gone on fire and smoke leakeing through walls into adjoping property, the squash court