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A simple and original mechanism to control the polarisation of uniform hybrid waveguide-planar leaky-wave antennas is proposed. The operation is based on introducing simple modifications of the planar dimensions of the structure cross-section, which is shown to control the horizontal and vertical components of the radiated fields. The proposed antenna dispenses with the need for periodic elements, commonly used in flexible polarised leaky-wave antennas, and therefore significantly reduces the design complexity. Parametric curves have been obtained to assist in the simple and efficient design of the proposed antenna. The novel mechanism is illustrated by means of several antenna prototypes operating at 5.7 GHz, producing linear, elliptical and circular polarisations. Commercial three-dimensional finite element method has been used for the simulations, and the results are validated with experimental testing.