Two very Clapham features of our Clapham garden are two Cordyline australis trees (originating from New Zealand). The green one was smack bang in the middle of the main bed and starting to lean out across the patio. In Feb while it was still cold but after frosts I moved it over to the back right corner to sit next to the dark red tree. Personally I think this helps add structure to one corner of the bed and contrasts nicely with the other tree.
If you’d like to move a Cordyline tree it’s much easier than other trees because the root forms one big ball near the base like a palm, so you just need to water heavily, dig around to find the root mass and clear soil without damaging the roots. Have the hole ready where you want to place it, carry over, surround with soil again to the same level, stamp down to firm up and water again. Do it in early spring while it’s still dormant. This is obviously easier to do when the tree is still small.
The good thing about Cordylines is that they grow tall on thin trunks allowing light to still reach the ground below for other plants.