Languages based on the theory of timed automata are a well established approach for modelling and analysing real-time systems, with many applications both in an industrial and academic context. Model checking for timed automata has been studied extensively during the last two decades; however, even now industrial-grade model checkers are available only for few timed automata dialects (in particular UPPAAL timed automata), exhibit limited scalability for systems with large discrete state space, and cannot handle parametrised systems, or systems with unboundedly many processes. Leveraging recent advances of general-purpose fixed-point engines, we present a flexible method for translating networks of timed automata to Horn constraints, which can then be solved via of-the-shelf solvers. The resulting analysis method is fully symbolic and applicable to systems with large or infinite discrete state space, can be extended to include various language features, for instance UPPAAL-style communication/broadcast channels and BIP-style interactions, and can analyse systems with infinite parallelism. Experiments with timed automata models demonstrate the feasibility of the method.