I would expect all Chile to be a part of this Argentina. Even Peru
The issue is that the Argentinean economy in the 19th Century depending a lot in trade with the UK so, while a British Argentina would have important political, demographical and military consecuences, it shouldn't make that much of a difference in the economy. That being said, if it can prevent the Argentinean civil war and exterminate the Mapuche indians earlier, that would increase the overall productivity of the British South America's economyYeah but if the US sells grain to Latin America, then Britain can keep Argentine grain for itself and doesn't have to buy from the US.
Britain is probably not going to project any influence much beyond Buenos Aires and the south shore of the Rio de la Plata until the wars in Europe are concluded.at which point native independence movements are likely to have taken root as per OTL and they may simply sponsor these...
They could also make a probe to try and acquire the Banda Oriental and Montevideo as well but lest assume that fails. They have enough going on in Europe to assume that at least the portenos will hang on there.
thus at the conclusion of the napoleons Wars you have the British likely to hang onto only Buenos Aires and its claims to Patagonia with an Argentine Republic to its north and northwest. Chile/Paraguay may or may not be there own republics as well as its unlikely the Spanish can project and reassert their control in the aftermath of events in Europe. Assume that the British invasion is the catalyst that spurs the Argentine independence. Further we can probably assume that Paraguay will be independent simply because of its distance from what is likely to be the centre of Argentine politcal control, Cordoba. Further have the same falling out between Centralists and Federalists and its easy to see Artigas perhaps hanging on east of the Parana (butterflies, perhaps British attempts at rapprochemont keep the Brazilians from interfering so Federalist and Centralists forces are better matched)
Is this enough to butterfly into more royalist or pro Spanish sentiment in Potosi, Charcas and La Paz or at least give them continued control of Peru and influence in these regions such that they formally split and fall back to Lima's control. British control of the BA and points along the coast, mostly just Carmen del Patagones and the rapprochemont with with Artigas butterflies to no Cochrane in Chilean service and the Spanish eke out a victory at Lima and the VR of Peru generally ( changing the geopolitical goals viz a viz New Spain/Mexico respectively) They will need a supply route across the isthmus of Panama or continuing influence in New Spain or Guatemala at least.
The Spanish perseverance to the north at least for a time ( who knows how long it will last, they are going to have to either devolve power at some point or lose it violently eventually. Since the Argentine Republic has no Ocean access except by river port at Rosario..Formal union of Chile with the Centralist Argentine Republic ( mind you Is that likely, they have the British to the south with claims on Patagonia conflicting with theirs and a continuing Spanish presence to the north and its at least a possibility)...Some kind of Road across the Andes to Santiago and Valparaiso is going to be of paramount importance.
Aftermath..immigration...Can we not suppose that some of the the at least English/Irish and Scottish emmigration ( during the 20's, 30's and 40's that went to the US could instead be directed to Buenos Aires. It is afterall far closer than Australia and the Pampas are within reach. And for the same reason that emmigration to BNA was encouraged in the aftermath of Wo1812, you probably will have similiar measures in BA. preventing encroachment by the Spanish speaking Argentines and securing the Br. presence on the Pampas and eventually Patagonia. By the way..Name, and not very original, but probably simply British South America as a collective term. La Plata Province for the British colony and Buenos Aires probably remains as the name of the city for the same reason that Quebec and Montreal remained after their conquest. Beyond that though names and borders will be far different.
Slower settlement of Australia ( perhaps even Australie Ouest) probably but perhaps a larger interest in South Africa later in the century.
thoughts?
Just to put things in perspective, the Bristish military campaign to conquer the region is, roughly speaking, this map.
Oh, and the Mapuches are probably fighting for the Spanish: they have offered assistance in OTL, and ITTL it would have been accepted. Unfortunately this map doesn't have a scale. As a reference the distance between Buenos Aires and the border with Chile is roughly 650 miles/1000 km
Not really very likely given the distances and number of troops which would have to be involved. The British would need a full-scale invasion force to get to Cordoba, I can see an assault on Cordoba after many years of consolidation on the River Plate, but just like that (in 1807), it would be ASB. Put simply, why would the British push so far in-land? There's nothing in it for them.
How about a British Uruguay (Just Montevideo initially) and Buenos Aires (city and surrounding area), invaded quickly in the 1806/07 fracas. This would lead to British control of the River plate and a consequent expansion round Cape Horn (Tierra del fuego, a colony somewhere near Rio Gallegos and another at Punta Arenas, maybe even Puerto Montt). However, the Argentine South would remain largely indigenous until the 1860's, the colonies being island cities in the vastness of the pampa, slowly expanding inland.
Then we see the war of the desert (but a less exterminatory version) with the submission of the Ranqueles and the Mapuches to the crown, but them receiving large tracts of land to govern under their own laws (around the 1880s?)
Southern Chile and Santa Cruz come under the Crown colony of Tierra del Fuego.
Uruguay, Entre Rios, Buenos Aires, Eastern Pampas and Eastern Patagonia are Dominion of The River Plate.
The North West down to Western Patagonia form a new state (Confederacion de Provincias Platenses?), possibly including Paraguay (nearly happened OTL, perhaps the British threat would push the Paraguayans into the Union). If Paraguay were involved, all of Misiones and Corrientes would be included in the new state, if not, they would go to Paraguay. This new state would have a substantial Amerindian feel, as Salta, Jujuy and Tucuman were largely Quechua at this time, and Paraguay, Misiones and Corrientes were Guarani-speaking.
Under British Argentina (if the 1806/07 British invasion was a success), the political geography of South America would be different. The most plausible scenario would be, Bolivia, Chile, Paraguay and Uruguay would not exist as a seperate nation. These countries would be part of British South America that later to be known as Argentina (I prefer Argentina than Plate because Plate is too literal and bad sounding). About Brazil, Brazil would be smaller than in OTL because same parts of Brazil are in British South America.
The most plausible immigration pattern if Argentina is a British colony would be different, most of the Spanish or Italian immigrants would rather go for Brazil because Argentina is a British colony and British is already assimilating the older Spanish settlers in Argentina although there's a significant Spanish or Italian immigrants in British Argentina after 1900s. From 1810 to 1880, almost all immigrants to Argentina (if the 1806/07 British invasion was a success) are British (English and Irish are the majority of the British immigrants while the Scottish and the Welsh are the minority). English and Irish immigrants are dominant in urban areas while the Scottish and Welsh are dominant in rural areas. After 1880, Germans, Spanish, Italians, Polish, Ukrainians, Scandinavians, Greeks and Croats are starting to dominate the immigration patterns to British Argentina. These immigrants, after several years, they are assimilated to the dominant British population.
lets see.. the Br. are involved heavily in the Wars of the Continent so no..they will NEVER get beyond holding BA and the adjoining lands of the the Plate if they're lucky. like 1812 this would be a side show to the main event on the continent.
the Br. invasion was in part catalyst for the drive to independence for the portenos. the British may take BA but the portenos will keep them from the interior, it will likely have the same effect with minor adjustments. Given a choice between rule by Britain or Rule by Spain, independent republic not an option...I think even the portenos of the Plate would prefer a return to Spain.
I just don't see the Br. taking the entirety of the VR La Plata. the Spanish position in what became Bolivia is almost certainly strengthened which strengthens their position in Peru generally at least for a time longer.
AuroraBorealis, your scenario is not for Argentina's potential. If the British conquered the Buenos Aires and Montevideo area, the British would move westward to get Cordoba, then northward for Tucuman, Potosi, and La Paz. I am very sure that all of the Viceroyalty of La Plata plus Chile would gone to British after the Congress of Vienna of 1815.