Should an indoor badminton facility with approx. four courts, some seating and a couple of vending machines be provided with fire extinguishers? The facility will be unsupervised, i.e. there will be no staff members. The general public will hire a court online, and let themselves into the building via a combination lock. That means there will be no 'trained' people to use extinguishers in the event of a fire. Is it advisable to NOT to provide extinguishers as people will simply exit the building in the event of a fire? Providing extinguishers might result in misuse, vandalism, etc.

I'd be grateful for any advice.

That's a decision for your fire risk assessment (which you must have, the law makes no differentiation whether there are staff there or not). The expectation is to provision, but as you can see below the law is worded such to allow flexibility.

 

From the legislation:

Fire-fighting and fire detection

13.—(1) Where necessary (whether due to the features of the premises, the activity carried on there, any hazard present or any other relevant circumstances) in order to safeguard the safety of relevant persons, the responsible person must ensure that—

(a)the premises are, to the extent that it is appropriate, equipped with appropriate fire-fighting equipment and with fire detectors and alarms; and

(b)any non-automatic fire-fighting equipment so provided is easily accessible, simple to use and indicated by signs.

(2) For the purposes of paragraph (1) what is appropriate is to be determined having regard to the dimensions and use of the premises, the equipment contained on the premises, the physical and chemical properties of the substances likely to be present and the maximum number of persons who may be present at any one time.