It's kind of hard to tell from the sample but you might check out Vinca minor.

Not Vinca minor. Apart from the appearance being different it would never survive that climate.

I'm thinking its some kind of tree - e.g. date. And given I've had two sprout up in my smallish garden, its probably regional.

Not a date, they come off palms. Sorry, no help on what it might be.

Calotropis?

Here is a link that might be useful: Calotropis

Not a date, they come off palms. Sorry, no help on what it might be.

Calotropis looks correct. It is growing two leaves at a time, and fits the other descriptions.