I was on a flight from Dublin to Leeds yesterday. Sat with a clear view of one engine.
Prior to takeoff I noticed that it was rotating anti-clockwise fairly slowly - I was sat behind it at a window seat & "looking through" the prop if you see my meaning. I then saw it slow down, stop for about 10 seconds & then start rotating clockwise - fairly quickly going up to a fast speed before we began taxiing.
Can anyone explain this - there must be a reason for it.
From what you describe, and as you were taxiing, I would say that the pilot was using one engine only, a not uncommon thing as far as my experience is concerned. The prop you were looking at was being feathered; in other words the engine was on idle and the prop was turning in the wind, hence going anti clockwise. Before take off the pilot would apply full power to that engine and thus then the prop would turn clockwise.
Used to see that a lot in the old days as a child, and especially when RAF Shackletons were flying on exercise across Malta, with one or even two props being feathered out of the four engines.

In modern times I often saw RAF Hercules feathering a prop or two.
PS Shackletons had twin conter rotating props per engine, so the effect was very interesting.