Angular distributions of the polarization and the cross section for $p\ensuremath{-}^{4}\mathrm{He}$ elastic scattering have been measured in 2-MeV steps between 20 and 45 MeV and in steps of approximately 150 keV across the 23.4-MeV resonance corresponding to the second excited state of $^{5}\mathrm{Li}$ at 16.7 MeV excitation. The relative uncertainties of the polarization measurements are typically less than \ifmmode\pm\else\textpm\fi{}0.01. The normalization uncertainty from energy to energy and relative to the older data below 20 MeV proton energy is approximately 2%. The cross-section angular distributions with a relative uncertainty of 3% have been normalized to previously existing data, since an absolute cross-section measurement was not feasible with our experimental setup. The polarization measurements provide an accurate proton polarization analyzer up to 45 MeV. With the exception of the narrow resonance region around 23.4 MeV, the analyzing power near ${\ensuremath{\theta}}_{\mathrm{lab}}=125\ifmmode^\circ\else\textdegree\fi{}$ exceeds 80% at all energies and shows no rapid variations. Around 30 MeV, a very weak and broad anomaly is seen in the polarization, coinciding in $^{5}\mathrm{Li}$ excitation (approximately 22 MeV) with the structure observed in $d\ensuremath{-}^{3}\mathrm{He}$ elastic scattering.