The tunnelling of a particle through a potential barrier is a key feature of quantum mechanics that goes to the core of wave-particle duality. The phenomenon has no counterpart in classical physics, and there are no well constructed dynamical observables that could be used to determine 'tunnelling times'. The resulting debate(1-5) about whether a tunnelling quantum particle spends a finite and measurable time under a potential barrier was reignited in recent years by the advent of ultrafast lasers and attosecond metrology(6). Particularly important is the attosecond angular streaking ('attoclock') technique(7), which can time the release of electrons in strong-field ionization with a precision of a few attoseconds. Initial measurements(7-10) confirmed the prevailing view that tunnelling is instantaneous, but later studies(11,12) involving multi-electron atoms-which cannot be accurately modelled, complicating interpretation of the ionization dynamics-claimed evidence for finite tunnelling times. By contrast, the simplicity of the hydrogen atom enables precise experimental measurements and calculations(13-15) and makes it a convenient benchmark. Here we report attoclock and momentum-space imaging(16) experiments on atomic hydrogen and compare these results with accurate simulations based on the three-dimensional time-dependent Schrodinger equation and our experimental laser pulse parameters. We find excellent agreement between measured and simulated data, confirming the conclusions of an earlier theoretical study(17) of the attoclock technique in atomic hydrogen that presented a compelling argument for instantaneous tunnelling. In addition, we identify the Coulomb potential as the sole cause of the measured angle between the directions of electron emission and peak electric field: this angle had been attributed(11,12) to finite tunnelling times. We put an upper limit of 1.8 attoseconds on any tunnelling delay, in agreement with recent theoretical findings(18) and ruling out the interpretation of all commonly used 'tunnelling times'(19) as 'time spent by an electron under the potential barrier'(20).