Ensuring accurate call prioritisation is essential for optimising the efficiency and responsiveness of mental health helplines. Currently, call operators rely entirely on the caller's statements to determine the priority of the calls. It has been shown that entirely subjective assessment can lead to errors. Furthermore, it is a missed opportunity not to utilise the voice properties readily available during the call to aid in the evaluation. Incorrect prioritisation can result in delayed assistance for high-risk individuals, resource misallocation, increased mental health deterioration, loss of trust, and potential legal consequences. It is vital to address these risks to guarantee the reliability and effectiveness of mental health services. This study delves into the potential of using machine learning, a branch of Artificial Intelligence, to estimate call priority from the callers' voices for users of mental health phone helplines. After analysing 459 call records from a mental health helpline, we achieved a balanced accuracy of 92\%, showing promise in aiding the call operators' efficiency in call handling processes and improving customer satisfaction.