This is the New Zealand Cabbage Tree (Cordyline australis) in the Lomandra Family (Lomandraceae)*. In the U.K. you may know it as the Torbay Palm, though you are correct, it is not a true palm. They are very distinctive and attractive trees. I grow several in my garden. There are also a number of cultivars with colored or variegated leaves.
* Lomandraceae, as Lomandroideae, is sometimes treated as a subfamily of the Asparagus Family (Asparagaceae).