What type of oolong is Twining's oolong? Or what would this be closest too?
From the UK site, it looks like it is also a type of Tieguanyin tea from Anxi in Fujian Province. Now Tieguanyin translates to "Iron Goddess of Mercy", so you are heading in the right direction.

I suspect, having had some incidental exposure to the tea manufacturing process for a different manufacturer, that the exact blend will be a matter of which farms they get the tea from, and which methods they use for preparation. These are likely single supplier farms - so they will only sell to Twinings or a handful of companies. It is said that teas have a terroir similar and even more complex than those ascribed to wines, so it could well be that the taste is down to the farms they have as suppliers.