Summary: This paper focuses on developing an efficient numerical approach based on Taylor-wavelets for solving three-point (nonlocal) singular boundary value problems. A special case of the considered problem, with strongly nonlinear source term, arises in thermal explosion in a cylindrical reactor. The existence of a unique solution is thoroughly discussed for the considered problem. To establish the current method, an equivalent integral equation is constructed for the original problem to overcome the singularity at the origin. The evaluation of derivatives appearing in the model is also avoided in this way. Moreover, this scheme skips the integrals while reducing them into a system of nonlinear algebraic equations. Unlike other methods, this new approach does not require any linearization, discretization, perturbation, or evaluation of nonlinear terms separately. To the best of our knowledge, this is the first application of the wavelet-based method to the considered problem. The formulation of the proposed method is further supported by its convergence and error analysis. Some numerical examples are solved to validate the efficiency and robustness of the proposed method. Further, the computational convergence rate (COR) is reported for the first few examples to assist the obtained numerical solution. Moreover, the obtained numerical results are compared with those of existing techniques in the literature.