Summary: We investigate the orthogonal packing of rectangular objects into a circular container of fixed radius. We propose a new constructive heuristic called which builds a feasible packing starting from an ordered list of rectangles. This decoding procedure is polynomial and permits to move from the permutations search space to the packings search space by means of simple combinatorial moves combined with powerful geometrical analytical forms. The procedure is integrated into two well known metaheuristics, namely, a variable neighbourhood search (VNS) and a simulated annealing (SA). Two variants, namely xVNS and xSA, which stand as accelerated versions of VNS and SA are also presented. The proposed methodology produces 32 new best solutions out of the 54 benchmark instances while requiring less computational effort than the state-of-the-art method. In addition, we conduct experiments on newly generated larger instances which we have made publicly available alongside their respective results obtained from the proposed metaheuristics.