Louisa May Alcott was (as is my wife) directly descended from Thomas Alcock, who with his brother George, came to Boston in Winthrop's fleet in 1630. Thomas was her 5th Great Grandfather.
If Thomas and George left a brother in England he would have been Louisa May's 6th Great Uncle.
It is not absolutely certain, but it appears they were from Sibertoft, England. The visitation of Sibertoft in 1618 lists a Thomas & George Alcock and their sister Elizabeth. Of course they might have had a brother born after 1618, or they might not be the Sibertoft Alcocks.
But in any case a brother left in England whose descendents went to Australia could have been no closer than Louisa May's 6th Great Uncle.
Louisa's line: Thomas Alcock = Margery Philip Alcock = Elizabeth Mitchell John Alcock = Susanna Heaton John Alcock = Deborah Blakeslee Capt. John Alcox = Mary Chatfield Joseph Chatfield Alcox = Anna Bronson Amos Bronson Alcott = Abigail May Louisa May Alcott