It's not a palm Malcolm, it is Cordyline australis aka New Zealand
Cabbage Tree. Cordylines are in the same family as the Yuccas, Agaves
and Phormiums and have closer affinities to the lily family. On the
other hand, true palms belong to an entirely different order of plants
and are not remotely related despite superficial similarities.

Cordylines are extensively planted in coastal regions and mild winters
over the past decade have enabled them to grow to a decent size
further inland. Cordylines are highly variable in flower, leaf width
and overall habit. Some have very narrow leaves, while others can
have leaves up to 9cms.acoss. Leaves can be gently arching to almost
stiffly erect and the flower spikes can be sparsely or densely
flowered, erect, horizontal or pendulous. Usually the flowers are
translucent white, but it is not unusual for them to be pink tinged
and a very fine form exists with larger flowers that are creamy,
almost yellowish-white.

The flowers give way to masses of small white berries that can remain
well into winter if the birds (jackdaws especially) leave them alone.
A Cordyline carrying its full compliment of berries is even more showy
than when in flower. As each growth produces a flower spike, new
shoots develop at the base of the spike eventually developing into new
heads of leaves that can take from 1 - 3 years to reach flowering
size. In time the Cordyline develops into a rather handsome,
branching 'tree' carrying many growths and several to many large
spikes of flower.

HTH.