Despite their widespread use in cell biology, fluorescence lifetime imaging microscopy (FLIM) data-sets are challenging to analyse, because each spatial position can contain a superposition of multiple fluorescent components. Here, we present a data analysis method employing all information in the available photon budget, as well as being fast. The method, called uFLIM, determines spatial distributions and temporal dynamics of multiple fluorescent components with no prior knowledge. It goes significantly beyond current approaches which either assume the functional dependence of the dynamics, e.g. an exponential decay, or require dynamics to be known, or calibrated. Its efficient non-negative matrix factorization algorithm allows for real-time data processing. We validate in silico that uFLIM is capable to disentangle the spatial distribution and spectral properties of five fluorescing probes, from only two excitation and detection channels and a photon budget of 100 detected photons per pixel. By adapting the method to data exhibiting Förster resonant energy transfer (FRET), we retrieve the spatial and transfer rate distribution of the bound species, without constrains on donor and acceptor dynamics.