Looking toward Circular Quay and the ferry terminal with the city in the background. Things on left and right you will recognise.
I would be interested to know if it works for you because I have tried some UK web cams and they are mostly still pics taken every few minutes though there were a few live movie cams - at the moment of wet grey seafronts - it's that time of year I suppose.
On the same website I found a video of the ship I went for my one (and only) cruise on leaving its berth.
Notice the pilot boat buzzing in circles keeping other craft out of the way. I was on a ferry yesterday coming from up the Parramatta River and it was hanging about under the Harbour Bridge presumably ready to do the same thing for the Radiance of the Seas which was berthed at the Quay.