Ultrafast terahertz (THz) spectroscopy is a potent tool for studying the fundamental properties of matter. Limitations of current THz sources, however, preclude the technique being applied in certain advanced configurations or in the measurement of e.g. strongly absorbing samples. In response to this problem, here we demonstrate the generation of 1.38 mW broadband THz radiation at 10 megahertz (MHz) repetition rate by combining the highly efficient nonlinear organic crystal HMQ-TMS with ultrafast pump pulses generated using a simple and stable external pulse compression of a high power, near-infrared (NIR) femtosecond ytterbium-doped fibre (Yb:fibre) laser. Utilising spectral broadening in a large core, polarisation maintaining photonic crystal fibre and a pair of SF11 prisms, we achieve a tenfold pulse compression of the Yb:fibre laser, yielding compressed 0.35 µJ pulses with a full-width at half maximum pulse duration of 22 fs, exerting a peak power of 13.8 MW at a repetition rate of 10 MHz. THz generation through optical rectification of the NIR pulses is explored in two distinct thicknesses of the organic crystal, leading to a maximum conversion efficiency of ∼5.5·10−4 , an order of magnitude higher than that achieved with inorganic nonlinear crystals, e.g. gallium phosphide, for similar pump parameters. The focused THz beam has a peak on-axis field strength greater than 6.4 kV·cm−1 in unpurged atmosphere. We believe that our moderately strong-field THz source is well suited to a variety of applications in ultrafast THz spectroscopy, in particular THz-enabled scattering-type near-field, and scanning tunnelling spectroscopy, where multi-MHz repetition rate sources are required.