We present sensitive, high angular resolution (6x 5 arcsec^2) lambda 21-cm observations of the neutral hydrogen in the nearby barred Seyfert galaxy, NGC 4151. These HI observations, obtained using the VLA in B configuration, are the highest resolution of this galaxy to date, and reveal hitherto unprecedented detail in the distribution and kinematics of the HI on sub-kiloparsec scales. A complete analysis and discussion of the HI data are presented and the global properties of the galaxy are related to the bar dynamics presented in Paper I. HI absorption, consistent with previous studies, is detected against the radio continuum nucleus and shows two components - a deep absorption component, centred at 987 +/- 1 km s^-1 and width 87 +/- 3 km s^-1, and a weaker component, redshifted to 1096 +/- 6 km s^-1 with a width of 35 +/- 15 km s^-1. An alternative fit is also presented. In addition to the absorption, a high velocity cloud is detected in emission, coincident with the nucleus. This cloud is redshifted by 260 km s^-1 from systemic, has an HI mass of 2.3 x 10^7 M_solar, and corresponds to outflow on the far side of the nucleus. Contrary to previous studies, no HI bridge is detected reaching from the shocks directly across the nucleus. Instead, the gas streams from the shocks on to smaller orbits and forms fingers of HI that wind around the nucleus, consistent with predictions from general numerical simulations of bars. These fingers correspond closely with dust arcs seen in optical studies and resemble nuclear features seen by others in weak barred galaxies such as M100. A new rotation curve is presented, extending to within 8 arcsec of the nucleus and showing a turnover at a radius of ~35 arcsec, which was previously undetected in lower resolution studies. The corresponding resonance curve and the properties of the shocks (Paper I) yield a bar pattern speed of 24.5 +/- 3.7 km s^-1 and one inner Lindblad resonance (ILR) at a radius of 2.8 +/- 0.6 kpc. Our observations, however, do not rule out the possibility of an inner ILR.