I'm not quite sure what really changes to allow British victory. They goofed and bungled the Buenos Aires invasion, but even if they hadn't, it's likely that the locals, and royalists coming from the Northern parts of the viceroyality are going to make the situation untenable for the British, especially once French invasion of Portugal gives Britain a European theatre to concentrate on.
But, magically giving Britain a lasting foothold in Buenos Aires/Montevideo (a more likely WI is WI Britain held on to Montevideo after getting booted out of BA): There's the whole likelihood of the hinterlands remaining untamed by the British (they barely had enough to take/keep BA IF everything went right). Portugal/Brazil does not take over and annex Uruguay, and hence does not lose it in the cisplatine war. This enhances Brazil's stability at the beginning of it's independance, and possibly allows Pedro I to keep control there instead of turning tail and running to Portugal. All this probably butterflies away the Paraguayan War, which in turn keeps Brazil on it's course of slow advancement with a small military/less republicanism, so Pedro II probably doesn't get the boot. Overall, this is probably a net plus for Brazil as it doesn't spend a lot of gold taking then losing Uruguay, both of which pissed off the Brazilian populace.
Additional affects: San Martin may not return to help the independance movement of Argentina/Chile/Bolivia/Peru, and/or concentrates on driving out the Brits. This butterflies away the crossing of the Andes and likely eliminates or delays Chile/Bolivian independance for a long while. Belgrano likely does not try to invade Paraguay, so Paraguayan actions are likely far different. Do they get the notion to go independant, or are they still under the illusion that they're part of the spanish realm?
While Portugal and England are nominal allies, England was never shy about using it's superior military status to take advantage of the weaker nation. I envision a beleagured Britain in Argentina, but if they did manage to make it a secure possession, being next door to Brazil makes it a little easier to muscle B about. Don't really see much changing from OTL, though.
Peninsular war doesn't change, but Britain does have a sticky situation trying to balance holding on to Spanish booty while helping Spain vs France.