The first response that comes to my mind is, it would be easier and cheaper just to hang their convicts rather than ship them to places that would kill them almost as surely.
In addition to getting felons out of Britain, and the deterrent to crime this terrible punishment provided, it also meant labor forces for various colonial schemes.
I imagine that people could be kept alive, in no great comfort to be sure, in coastal Antarctica or on some of the islands around--provided food and other necessities were constantly being shipped in. But I don't see how the transportees could possibly feed themselves, let alone have any surplus labor left over for some money-making enterprise. If they are to be fed, the cost would be high, and there had better be some highly profitable product they could make with all the time freed up by having their food hauled to them, to pay for it.
Considering that we are coming up on 250 years since Cook first sighted the last continent, and in all that time no one I can think of has ever based any sort of profitable enterprise on Antarctic resources, except perhaps a few whalers and seal-hunters, I have to doubt that the late 18th century British authorities would be more clever.