Recurring outbursts associated with matter flowing onto compact stellar remnants (black-holes, neutron stars, white dwarfs) in close binary systems, provide strong test beds for constraining the poorly understood accretion process. The efficiency of angular momentum (and thus mass) transport in accretion discs, which has traditionally been encoded in the $alpha$-viscosity parameter, shapes the light-curves of these outbursts. Numerical simulations of the magneto-rotational instability that is believed to be the physical mechanism behind this transport find values of $alpha sim 0.1-0.2$ as required from observations of accreting white dwarfs. Equivalent $alpha$-viscosity parameters have never been estimated in discs around neutron stars or black holes. Here we report the results of an analysis of archival X-ray light-curves of twenty-one black hole X-ray binary outbursts. Applying a Bayesian approach for a model of accretion allows us to determine corresponding $alpha$-viscosity parameters, directly from the light curves, to be $alpha sim$0.2--1. This result may be interpreted either as a strong intrinsic rate of angular momentum transport in the disc, which can only be sustained by the magneto-rotational instability if a large-scale magnetic field threads the disc, or as a direct indication that mass is being lost from the disc through substantial mass outflows strongly shaping the X-ray binary outburst. Furthermore, the lack of correlation between our estimates of $alpha$-viscosity and accretion state implies that such outflows can remove a significant fraction of disc mass in all black hole X-ray binary accretion states, favouring magnetically-driven winds over thermally-driven winds that require specific radiative conditions.
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