A combustion chamber arrangement comprises an annular combustion chamber, a plurality of circumferentially arranged vanes and a radially inner sealing ring. The vanes are arranged at the axially downstream end of the annular combustion chamber. Each of the vanes comprises an aerofoil extending radially between a radially inner platform and a radially outer platform. The radially inner sealing ring forms a seal between a downstream end of a radially inner annular wall structure of the combustion chamber and the radially inner platforms of the vanes. A portion of the axial length of the radially inner sealing ring comprises a radially inner wall and a radially outer wall spaced radially from the radially inner wall to define a chamber. The radially inner wall has apertures to supply coolant into the chamber and the radially outer wall has effusion cooling apertures to supply coolant onto the surface of the radially outer wall.