Beyond Guiana: Britain's American Empire

In 1809 a Portuguese-British naval squadron took Guinana from the French. They gave it back in 1814...but what if they hadn't? Suppose the Portuguese had decided to let Britain keep Guinea to keep out the French, and it became a British colony?

Would it have been possible for Britain to use Guiana as a base to expand further into South America, perhaps say after Brazilian independence in 1822 (perhaps Dom Pedro forms an alliance with Great Britain, or dies early)?

What would South America (or a good portion of it) have looked like under British rule?
 
In 1809 a Portuguese-British naval squadron took Guinana from the French. They gave it back in 1814...but what if they hadn't? Suppose the Portuguese had decided to let Britain keep Guinea to keep out the French, and it became a British colony?

Would it have been possible for Britain to use Guiana as a base to expand further into South America, perhaps say after Brazilian independence in 1822 (perhaps Dom Pedro forms an alliance with Great Britain, or dies early)?

What would South America (or a good portion of it) have looked like under British rule?
If Britain keeps French Guyana, I think that it would probably return OTL British Guyana to the Dutch, because Britain would get everything it wanted from French Guyana, wich it could get from Biritish Guyana. Of course it is also possible that Britain decides to keep all of Dutch Guyana (including Surinam) to form a large British Guyana, but I suspect that the Netherlands would be compensated in some way (probably with a couple of French colonies like French st Martin and other islands).
 
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