Looks like a Livistona decipiens (also called decorum) to me. They are pretty easy to care for. They love lots of sun and get a little streched out indoors. Make sure not to let it dry out too much although it can handle moderate drought. Your's looks very nice and healthy!
-Alex

Hmmm... not seeing any teeth long the petioles... and trunk looks a tad fibrous. My guess is a Trachycarpus fortunei... any closer shots available? Either way, the more light, the better.

Many thanks for the kind and quick replies. I am attaching two more photos of some close-ups of the stem/trunk and some of the leaves (fronds... sorry, not up on my terminology). Any further ideas will be much appreciated.

Another close up shot. Basically, my concern is light levels and water. Soil seems to drain ok but not sandy at all. Many thanks again!