This article presents a Kalman filter based adaptive disturbance accommodating stochastic control scheme for linear uncertain systems to minimise the adverse effects of both model uncertainties and external disturbances. Instead of dealing with system uncertainties and external disturbances separately, the disturbance accommodating control scheme lumps the overall effects of these errors in a to-be-determined model-error vector and then utilises a Kalman filter in the feedback loop for simultaneously estimating the system states and the model-error vector from noisy measurements. Since the model-error dynamics is unknown, the process noise covariance associated with the model-error dynamics is used to empirically tune the Kalman filter to yield accurate estimates. A rigorous stochastic stability analysis reveals a lower bound requirement on the assumed system process noise covariance to ensure the stability of the controlled system when the nominal control action on the true plant is unstable. An adaptive law is synthesised for the selection of stabilising system process noise covariance. Simulation results are presented where the proposed control scheme is implemented on a two degree-of-freedom helicopter.