We consider S = 1/2 antiferromagnetic Heisenberg chains with alternating bonds andquenched disorder, which represents a theoretical model of the compound CuCl2xBr2(1−x)(γ −pic)2. Using a numerical implementation of the strong disorder renormalization group methodwe study the low-energy properties of the system as a function of the concentration, x, andthe type of correlations in the disorder. For perfect correlation of disorder the system is in therandom dimer (Griﬃths) phase having a concentration dependent dynamical exponent. Forweak or vanishing disorder correlations the system is in the random singlet phase, in whichthe dynamical exponent is formally inﬁnity. We discuss consequences of our results for theexperimentally measured low-temperature susceptibility of CuCl2xBr2(1−x)(γ − pic)2.