I think the farthest south the British got was Belize back in their Colonial days.
Not sure of the Islas Malvinas/Falklands history. I think, though, it was to encourage settlement. There might be a few sheep ranches there...
British Guyana actually shares a border with Venezuela...but Hugo is still full of crap.
There was an expedition against either Buenos Aires or Montevideo around 1803-7, somewhere in there, during the Napoleonic Wars. Bonaparte had put a family member on the Spanish throne and Spanish possessions were viewed as fair game.
The expedition was launched independently of London, from the Cape Colony in South Africa, recently won from the Dutch, also a French ally.
I think there was some kind of grand strategic plan to link up with the Portuguese in Brazil and divvy up Spain’s South American Empire, Portugal being a British ally since the 15th or 16th century.
Alas, after initial success against the Spanish colonial regulars the expedition came to a bad end, bogged down in street fighting against an aroused populace.
Once the British had extricated their forces London laid down the law, no more free lance, free-booting expeditions on local iniative. Not that that stopped such affairs, they continued, but as local border wars on the periphery of empire against native states, no more trans-oceanic campaigns w/out checking with home first!
‘Course if things had turned out differently there would have been awards, titles, honors and loot all ‘round...