According to Wikipedia, Chile, Argentina and Brazil have the largest British and Irish descended populations in Latin America. In the 19th century, farmers, miners, merchants and professionals were attracted to those countries. Those in the military also went there, as well as people who wanted to travel and explore.
Argentina attracted the most migrants from the British Isles, including Irish sheep farmers, Scottish beef farmers and a group of Welsh pioneers who famously settled in Patagonia, on the southern tip of Argentina, in the hope of protecting their way of life. These 200 Welsh settlers voyaged across the Atlantic on the tea-clipper Mimosa, arriving on 27 July 1865. Their settlement was slow to establish but it did succeed - and it is estimated that today at least 30,000 people speak Welsh in Argentina as a consequence.
What can you find out about ancestors who went to South America? There are databases online which seek to collect lists of residents who came from Europe, including the British Isles. It may also be possible to find your ancestors in census or church records. They also probably arrived by a port such as Buenos Aires and it is sometimes possible to find a record of their arrival. See the links below to get started:
FamilySearch Research Wiki – an overview of South American genealogy records including Catholic registers and census returns: https://familysearch.org/wiki/en/South_America
Links to South American research resources:
South American Brits database of 26,000 names:
Irish passengers to Argentina: 1822-1929; an online database of over 7000 individuals put together by the Society for Irish Latin American Studies (SILAS) using various sources with a name index:
An indexed collection of records from Argentina documenting the presence of thousands of Anglophone residents:
This website also includes a section on the Welsh Patagonians, including a name list: http://www.argbrit.org/Patagonia/mimosa.htm
Links to searchable databases of Irish and British settlers:
Scots in Argentina website – which includes lists of Scottish emigres, historical background and links to resources: