There may be a problem with the lead flashings around the chimney where it protrudes through the roof tile, this can allow rainwater to bleed through along the chimney breast. These will need to be reset if loose, they could be sealed in place if it is minor using a lead sealant similar to silicon mastic.
Cracks in the brick or blockwork can cause the fumes to escape, especially if it is a flueless chimney. You would need to identify where the smoke and soot are escaping and seal the leak. This could be done by replastering the chimney with sand and cement as this will achieve an airtight seal.
Ideally you would look at inserting a flue liner to the chinmey shaft and sealing it into the fireplace. This is possible to do in some situations and would avoid the future risk of more leaks.