Single molecule localization microscopy (SMLM) methods produce data in the form of a spatial point pattern (SPP) of all localized emitters. Whilst numerous tools exist to quantify molecular clustering in SPP data, the analysis of fibrous structures has remained understudied. Taking the SMLM localization coordinates as input, we present an algorithm capable of tracing fibrous structures in data generated by SMLM. Based upon a density parameter tracing routine, the algorithm outputs several fibre descriptors, such as number of fibres, length of fibres, area of enclosed regions and locations and angles of fibre branch points. The method is validated in a variety of simulated conditions and experimental data acquired using the image reconstruction by integrating exchangeable single-molecule localization (IRIS) technique. For this, the nanoscale architecture of F-actin at the T cell immunological synapse in both untreated and pharmacologically treated cells, designed to perturb actin structure, was analysed.