The ratio of branching fractions of the radiative B decays B-0 -> K-*0 gamma and B-s(0) -> phi gamma has been measured using an integrated luminosity of 1.0 fb(-1) of pp collision data collected by the LHCb experiment at a centre-of-mass energy of root s = 7 TeV. The value obtained is B(B-0 -> K-*0 gamma)/B(B-s(0) -> phi gamma) = 1.23 +/- 0.06 (stat.) +/- 0.04 (syst.) +/- 0.10 (f(s)/f(d)), where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is associated with the ratio of fragmentation fractions f(s)/f(d). Using the world average value for B(B-0 -> K-*0 gamma), the branching fraction B(B-s(0) -> phi gamma) is measured to be (3.5 +/- 0.4) x 10(-5). The direct CP asymmetry in B-0 -> K-*0 gamma decays has also been measured with the same data and found to be A(CP)(B-0 -> K-*0 gamma) = (0.8 +/- 1.7 (stat.) +/- 0.9 (syst.))%. Both measurements are the most precise to date and are in agreement with the previous experimental results and theoretical expectations. (C) 2012 CERN. Published by Elsevier B.V. All rights reserved.