A friend of mine showed me this trick.
First, take a tea towel, preferably a large one, and fold it lengthways. Put the cake, on a cake board, in the middle. Hold the two ends of the tea towel and use it to lift the cake into the tin. The cake in the picture is royal iced so I could tuck the tea towel in the side with no damage. If your cake is iced down the side in something soft, I have also used a long strip of brown paper as it will stay folded up the side of the box.