We are renting a warehouse space for a short 3month period. Does the owner of the premises have to provide us with a working fire alram for the building?

It will depend on the tenancy agreement who responsible for providing any necessary facilities however when the premises is occupied the Responsible Person under the Regulatory Reform (Fire Safety) Order 2005 will be responsible for implementing article 8 to 24 of the order which includes providing a fire alarm. However the owner could also be responsible for implementing certain articles in the order as a person having control which again could include providing a fire alarm.