An islanded microgrid includes a combined heating and power system as well as electric vehicles. It is a key method for increasing energy efficiency, reducing pollution, and achieving carbon neutrality. Considering the uncertainties caused by renewable energy, load, and electric vehicles, this study presents a modified tri-stage scheduling method to realise the real-time dispatch of the islanded microgrid. The novel tri-stage scheduling method incorporates an information feedback mechanism into the traditional tri-stage scheduling method to address the problem of the sub-optimal solution obtained by the traditional method, which results from the significant errors between the day-ahead forecast data and intraday forecast data. In addition, users are guided by the tri-stage real-time price to charge/discharge electric vehicles orderly to fill in the valley and shave the peak of the electric load. In this study, a quantum adaptive sparrow search algorithm is proposed based on the characteristics of the tri-stage scheduling optimisation model and the limitation that the original algorithm easily falls into a local optimum. In the case study, the superiority of the novel tri-stage scheduling method, modified algorithm, and orderly charging/discharging of electric vehicles proposed in this paper are evaluated in different seasons. In the vehicle-to-grid mode, the influence of different numbers of electric vehicles on the real-time dispatch of the islanded microgrid is analyzed and discussed.