Health monitoring of railway bridges under train loads is of importance for the assessment and maintenance of railway infrastructure. The existing dynamic methods for the estimation of axle loads of trains require the track irregularities that are difficult to be obtained. Additionally, as trains have multiple carriages with a large number of axle loads without knowing magnitudes and positions, the corresponding estimation problem is essentially ill-conditioned. Furthermore, only the estimation of train loads is considered in the existing methods. The ill-conditioning problem may further deteriorate when the structural identification of railway bridges is taken into account. To address these problems, a Bayesian probabilistic approach for the real-time simultaneous estimation of train loads and structural parameters of railway bridges is developed using only strain measurements. From the train-track-bridge interaction dynamics, the axle loads of trains are modelled as modulated filtered noises, which avoids the direct analysis of the coupled system and thus does not require the additional information of track irregularities. Additionally, the time-varying speed parameter is introduced for the position tracking of axles, which allows the axle detection for the train loads with variable speeds. Furthermore, in order to tackle the ill-conditioned estimation problem, the prior information on axle loads from standardized trains is incorporated into the extended Kalman filter (EKF) to reduce the number of unknowns and improve the estimation. Examples for the estimation of a single-span bridge and a multi-span bridge under train loads are presented to illustrate the feasibility of the proposed methods.