Harold Henry Joachim was the son of Henry Joachim, a wool merchant from London. He was a prominent philosopher who taught at St Andrews and Oxford, and also a talented violinist.
Harold was the nephew of the violinist and composer Joseph Joachim, who had a deep influence on his life. Joseph considered him one of his closest friends and confidents, and they exchanged numerous letters in which they discussed family matters as well as professional and artistic subjects. Joseph kept contact with his nephew during his tours around Europe, and made sure to visit him whenever he was in London or Oxford. In 1907, Harold married Joseph's daughter Elizabeth, and they had a son and two daughters.