I run a private members club which currently has no fire detection equipment (we also live here. Should the club legally have a fire alarm?

The part of the premises occupied by you will be a domestic premises and exempt from The Regulatory Reform (Fire Safety) Order 2005 but the part of the premises members have access to, will be subject to the Fire Safety Order. Whether a fire alarm is required will be determined by your fire risk assessment which is required by the order.

Check out http://www.firesafe.org.uk/regulatory-reform-fire-safety-order-2005/ 

Edited September 17, 201510 yr by Tom Sutton

If the accommodation (which presumably is staff accommodation that comes with the job) is within the club building and not separate is highly likely that a fire detection & alarm system will be required, although there are limited circumstances (that should be determined by Fire Risk Assessment) that could preclude it. Many pubs with accommodation for the manager or licensee have faced enforcement action for lack of adequate fire detection & warning systems and/or insufficient structural protection of the means of escape. Whilst parts of the premises may be considered not covered by the Fire Safety Order, they would be affected by those parts that do and so contain relevant persons who must be protected.

The lack of even a rudimentary manual fire alarm system (call points and sounders only) is suggestive that the premises are very small - if they are not you have to consider if a fire warning could be adequately given manually - would someone shouting fire be clearly heard instantly through all parts of the premises?