We present a catalogue of dense cores and filaments in a $3.8^\circ \times 2.4^\circ$ field around the TMC1 region of the Taurus molecular cloud. The catalogue was created using photometric data from the Herschel SPIRE and PACS instruments in the 70, 160, 250, 350, and 500 μm continuum bands. Extended structure in the region was reconstructed from a Herschel column density map. Power spectra and probability density functions (PDFs) of this structure are presented. The PDF splits into lognormal and power-law forms, with the high-density power-law component associated primarily with the central part of TMC1. The total mass in the mapped region is 2000 M$_\odot$, of which 34 per cent is above an extinction of $A_V\sim 3$ mag - a level that appears as a break in the PDF and as the minimum column density at which dense cores are found. A total of 35 dense filaments were extracted from the column density map. These have a typical full width at half-maximum (FWHM) width of 0.07 pc, but the TMC1 filament itself has a mean FWHM of $\sim 0.13$ pc. The thermally supercritical filaments in the region are aligned orthogonal to the prevailing magnetic field direction. Derived properties for the supercritical TMC1 filament support the scenario of it being relatively young. A catalogue of 44 robust and candidate prestellar cores is created and is assessed to be complete down to 0.1 M$_\odot$. The combined prestellar core mass function for the TMC1 and L1495 regions is well fit by a single lognormal distribution and is comparable to the standard initial mass function.