Complex sentence: In December 1944 he recorded "Quite Early One Morning" produced by Aneirin Talfan Davies again for the Welsh BBC but when Davies offered it for national broadcast it was turned down by BBC London.
Split into simpler sentences: In December 1944 he recorded "Quite Early One Morning", again for the Welsh BBC. This was produced by Aneirin Talfan Davies, but when Davies offered it for national broadcast it was turned down by the BBC London.