LONDON — Larry Sanders, the brother of Senator Bernie Sanders, is running to fill the seat being vacated by David Cameron, the former prime minister, in the British Parliament.

Mr. Sanders, 82, was chosen on Thursday night by the Green Party as its nominee in an Oct. 20 special election in the constituency of Witney, about 67 miles west of London.

Like his younger brother, Mr. Sanders grew up in New York City and attended James Madison High School and Brooklyn College. In 1969, after graduating from Harvard Law School, he moved to Oxford, England, where he has devoted his career to social work and the law and been an advocate in areas like mental health and education.

The brothers are close and share progressive political views. At an emotional moment during the Democratic National Convention in Philadelphia in July, Larry Sanders, as a delegate representing Democrats who live abroad, cast a vote for his brother, saying their parents would have been “immensely proud” of him.