This is a fascinating subject which I'd like to more research on, but good sources are limited and very expensive.
For example, the Kindle edition of this book is $30, an outrageous price for a digital book.
The British in Argentina: Commerce, Settlers and Power, 1800–2000 (Britain and the World)
The British in Argentina: Commerce, Settlers and Power, 1800–2000 (Britain and the World)
www.amazon.com
This tantalising article has a very expensive paywall:
The British in Argentina | History Today
I'll be reading this one shortly:
http://www.danielschavelzon.com.ar/ebooks/Historical_Arch_47_Schavelzon.pdf
More:
Britain and the Making of Argentina
www.britishempire.co.uk
The academic tomes tend to be very expensive...