We report a simple method for generating large hydrated clusters of alkali metals by 532 nm laser desorption of frozen solutions of Na/K salts in water. Na/K(H2O)(n) clusters with n higher than 30 are observed by UV photo-ionisation and time-of-flight mass spectrometry. We give a characterisation of the laser desorbed volume (related to the optical and thermal properties of the desorbed material) and a size and velocity distribution analysis of the clusters produced. A moderate supersonic expansion (M = 1.7) is evidenced. Using a Knudsen-layer model, a sample temperature of approximate to 530 K is deduced, consistent with a phase explosion process.