Hi Ken,
Pure speculation on my part but I would say prisoners from Newgate probably went by cart or wagon to Portsmouth due to the number of prisoners in Newgate. Once on the hulk York I doubt they would have been brought back to London to embark on the ship to Australia but that the ship would have sailed around to Portsmouth and picked them up there. If there is a surviving Surgeons Journal for the voyage of the particular ship you are interested in it might give details of where and how the convicts were embarked.
Convicts leaving the hulk to work on projects would have been rowed, or had to row themselves, to the jobs they were required to do. Times spent on hulks varied considerably according to how long it took to get ships ready for the long voyage to Australia, the health of the prisoner, the trade skills of the prisoner, the jobs requiring to be done ashore, the weather conditions at the time, the state of seaworthiness of the ship, the time it took to press gang a crew to sail the ship etc. All in all I think life on the hulks was horrific. A cruel, dirty, disease ridden, immoral hell on earth.

Andcarred