Its always difficult trying to envisage the situation without a photo or floor plan, but I will offer the following; you mention a small window in the kitchen, is it possible that an exit door could be provided at this window opening to ultimate escape at ground level?
I take it that the premises is provided with functional & apprpriate AFD
Water mist is not an entire solution as it is designed to contain a fire, (although experience shows that most systems will succesfully extinguish a small fire). By virtue of a basement, the smoke, heat and flame is trying to use the same escape route as the occupants, (upwards), has any thought gone into providing natural or mechanical venting in event of fire that directs the products of combustion away from the means of escape?
Finally, a bit radical, but the basement is not the best place for the kitchen in a HMO, can it be sited elsewhere, (this option may be cheaper than installing a water mist system)
Hope this is of some use