The artist Eppo Doeve painting the Martineau children at “Old Lodge in Terlow (Buckinghamshire),” Great Britain, July 1954, by Willem van de Poll, via Nationaal Archief (Netherlands).
I have not been able to find out anything about these siblings or the home. I cannot find an Old Lodge in Terlow, Buckinghamshire, or indeed a Terlow anywhere in Great Britain. The Martineau family is quite important in Birmingham (an ancestor of the Duchess of Cambridge was a Martineau), but apparently not in Buckinghamshire. Perhaps the photographer made some mistake in his notes.
The son on the right seems to have three golf balls between his fingers. A young amateur champion?
Alan or Robert (Jr.) Brebner on the homestead, Spruce Grove, Alberta, ca. 1905, via Provincial Archives of Alberta (both photos).
Robert McKay Brebner, a farmer and amateur photographer, immigrated from Scotland to Alberta in 1882 and secured a homestead in Spruce Grove. About 1894, he married Emily Wrench, and after the birth of their first child, Alan, in 1896, they built a two-story house. Robert died suddenly in 1909, and Emily ran the farm with hired help until Alan could take it over at the age of 17.