Keep in mind that Argentina was one of the 10th richest countries in the world at the turn of the 20th century, and attracted waves of immigrants not unlike the US. It was the policies of the mid 20th century that sent Argentina off track, economically.
Argentina was, for much of the 20th c., virtually a second ‘economic empire’ for Britain. We had large investments in there, and a good deal of influence.
What, you mean, incessant demands for the "re"conquest-and-annexation of “Southern Peru” or “Lower Uruguay” or “Greater Brazil”?
I wonder who’d end up getting Australia & New Zealand? The Dutch, the French, the Spanish, or the Portuguese?
Australia’s huge, like, the size of the Lower 48 States, and seacoast all around . . . It’s not inconceivable that more than one country would colonize it, at difference places along the shore. That would make for an interesting history.
I wonder what effect a major British colony in South America would have had on the colonization of Africa. If Britain had established a colony in Argentina in the 18th century they could have used it as a base for colonizing Africa in the 19th century. If Britain had controlled Argentina, South Africa, and Australia/New Zealand, they’d have essentially had control of all southern ocean trade routes.
They did control the Southern Trade routes in the 19th century anyway.
I do not think a British South America has much of an impact on reduction of colonial attempts elsewhere. The British colonial Empire was not expanded directly due to the Crown until the scramble for Africa. The impetus was alway through private persons and companies.
Drake’s (hypothetical in this AH) vision, as stated in the OP.
Also, come to think of it, in this AH, Britain, having control of all inhabited Antipodal territories, would also have undisputed claim to Antarctica . . . for what it’s worth . . .
I mean Silverland’s society in general would resemble the Falkland Islands’. I don’t know about how things would have worked economically, though.
My guess would be the Dutch. Weren’t they the first Europeans to colonize Tasmania (a.k.a. Van Diemen’s Land?)