We present the CAlibrating LYMan-{alpha} with H{alpha} (CALYMHA) pilot survey and new results on Lyman {alpha} (Ly{alpha}) selected galaxies at z~2. We use a custom-built Ly{alpha} narrow-band filter at the Isaac Newton Telescope, designed to provide a matched volume coverage to the z=2.23H{alpha} HiZELS survey. Here, we present the first results for the COSMOS and UDS fields. Our survey currently reaches a 3{sigma} line flux limit of ~4x10^-17^erg/s/cm^2^, and a Ly{alpha} luminosity limit of ~10^42.3^erg/s. We find 188 Ly{alpha} emitters over 7.3x10^5^Mpc^3^, but also find significant numbers of other line-emitting sources corresponding to HeII, CIII] and CIV emission lines. These sources are important contaminants, and we carefully remove them, unlike most previous studies. We find that the Ly{alpha} luminosity function at z=2.23 is very well described by a Schechter function up to L_Ly{alpha}_~=10^43^erg/s^ with L*=10^42.59(10^42.75^-10^42.01^)erg/s, {phi}*=10^-3.09^(10^-3.43^-10^2.95)Mpc^-3^ and {alpha}=-1.75+/-0.25. Above L_Ly{alpha}_~=10^43^erg/s, the Ly{alpha} luminosity function becomes power-law like, driven by X-ray AGN. We find that Ly{alpha}-selected emitters have a high escape fraction of 37+/-7 per cent, anticorrelated with Ly{alpha} luminosity and correlated with Ly{alpha} equivalent width. Ly{alpha} emitters have ubiquitous large (~=40kpc) Ly{alpha} haloes, ~2 times larger than their H{alpha} extents. By directly comparing our Ly{alpha} and H{alpha} luminosity functions, we find that the global/overall escape fraction of Ly{alpha} photons (within a 13kpc radius) from the full population of star-forming galaxies is 5.1+/-0.2 per cent at the peak of the star formation history. An extra 3.3+/-0.3 per cent of Ly{alpha} photons likely still escape, but at larger radii.