In this work we propose, analyse, and demonstrate a new adjoint-based multilevel multifidelity Monte Carlo framework called FastUQ. The framework unifies the multifidelity analysis of Ng 1 , multilevel multifidelity analysis of Geraci 2 and an adjoint error correction surrogate model due to Ghate 3. The optimal mean squared error estimator shows that introducing multilevel in a multifidelity framework guarantees reduction in computational cost. Moreover, unlike the surrogate model of Ghate 3 , the method does not suffer from the curse of dimensionality. FastUQ is demonstrated here to quantify uncertainties in aerodynamic parameters due to surface variations caused by the manufacturing processes for a highly loaded turbine cascade. A stochastic model for surface variations on the cascade is proposed and optimal dimensionality reduction of model parameters is realised using goal-based principal component analysis considering the adjoint sensitivities of multiple quantities of interest (QoI). The proposed method achieves a reduction of 70% in computational cost in predicting the mean quantities like total-pressure loss and mass flow rate compared to state-of-art MLMC method. The robustness of the method is shown in application to the highly non-linear case of a heavily loaded turbine cascade operating at off-design conditions.