Ive just taken over as the govener for H&S at my kids playschool.

its a small single story building comprising of 3 linked rooms with a fire exit at either end.

Both fire exits are locked the an old style mortise lock (the large key type) which is hung up on a nail on the back of the door in question.

Also there is a security chain at high level fitted to the door to stop any escaping kids (The kind fitted to flats)

is this acceptable? or should it have a single means of exit such as a strike bar? however the door also opens inwards.

I would say it is not acceptable, as all doors need to be easily opened, without the need of a key, in an emergency, during the time a premises is occupied. There are devices that are acceptable which provides delayed exit and others that warn the staff that a door has been opened, check out https://www.firesafe.org.uk/security-and-fire-safety/ and https://www.safelincs.co.uk/fire-exit-door-security-seal/?q=security. The doors should open in line of escape if it is likely to be used  by more than 60 persons but panic bars/pads are not always required it depends on the circumstances.

Without a detailed layout of the premises it is not possible to give a definitive answer to your problem and it needs to be properly fire risk assessed to achieve that.