David,
All of the golf clubs established at the end of the 19th century in Argentina were founded by British (mainly officers of the railroad companies). For example, the Mar del Plata Golf Club (the first set of photos) was founded by the Agar brothers, John Drysdale, V. Scroggie, Frank Henderson and Robert Paton. The San Andrés Golf Club, to which the third clubhouse posted belongs (which means Saint Andrews in Spanish) was also founded Valentine Scroggie and his friend V.H. Masters. The flag of the Club is the St. Andrews cross. Its course was laid out by Mungo Park, son of Willie Park.
The Hurlingham Club (photos to come) was founded in 1888 by John Ravenscroft. As you see, they were all British. There are many more clubs that were founded by British.
The first truly Argentine golf club (which means founded by Argentines) was the Golf Club Argentino. But the British influence was very strong even in those clubs that were not founded by British and all of them tried to imitate what they saw in Britain.