Hello and thanks for using Just Answer.
I am Al and am happy to assist you with your enquiry.
It's a legal requirement for all blocks of flats (including houses converted into
two or more flats) to have a fire risk assessment of the communal areas only.
But this must include the front doors of individual flats. The responsibility
to arrange the assessment lies with the landlord.
However, in a similar way as you probably pay to the Management Company a proportion of the block Buildings Insurance, and possibly service charge on a regular basis or whenever communal repairs are required, the cost involved in implementing any necessary fire safety measures is the ultimate responsibility of the Leaseholders, under the terms of their Lease.
This is because 99 out of 100 Leases will stipulate that you will reimburse the Landlord for any costs incurred by them in maintaining the communal areas and the property as a whole. Your Lease will also no doubt state that you will comply with all legislation, and if the fire risk assessment has recommended fire alarms, you would be caught unde this.
If you have any doubts, I suggest that you ask the Management Company for evidence that you are under a duty to pay your proportion (as I have not seen your Lease to confirm), but I would be most surprised if you ar enot responsible, I am afraid to say.
Sorry this is not the answer you were looking for, but hope I have set out the legal position.