Borchardt was born in Brandenburg, Germany. He studied medicine at the University of Berlin, qualifying in 1838. He worked at Breslau in eastern Germany, and played a major role in the medical relief effort during a typhus epidemic in 1845. Borchardt was politically active during the 1848 revolutions and was imprisoned for his beliefs. On release, he migrated to Britain, living first in Bradford, and then moving to Manchester in 1852.
Borchardt enjoyed great success in Manchester. Apart from his private work he was also honorary physician to the General Dispensary for Children. He helped establish a larger hospital in Bridge St. in 1860 (the hospital later became the Royal Manchester Children's Hospital, and moved to Pendlebury on the outskirts of Manchester in the 1870s). Borchardt's political enthusiasms had mellowed in later life; he was an active Liberal, but was also acquainted with Marx and Engels, who perhaps predictably did not have a high opinion of him.