Hi Eustace,
In 1828, like now for instance, the government was looking for ways to reduce costs, so the Lord High Admiral of the Navy gave instructions that in Naval dockyards the work done by horses should be replaced by convicts. So maybe your relative, before starting his trip to Australia, for for a time in the dockyards.
According to a newspaper report written in 1828, one of the prisoners, a man called Jas. Hawkins, a notorious character, managed to disengage himself from his irons, jumped out of the caravan and made good his escape. On checking the other prisoners, most of them were about to do the same. The newspaper article reported that on publication date Hawkins had not been re-captured. Hawkins was being transported from Newgate to a ship at Sheerness.
I am sure that walking would allow great opportunity to escape.
I have read many account sheets in the papers between those dates and there are bills quoted "for the conveyance of Prisoners". Unfortunately not show how!
Tom