Tennant was the brother of Margot Asquith (née Tennant), the wife of the prime minister.
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On her overseas trips she became closely acquainted with influential British women such as Margaret Lloyd George, Margot Asquith, Clementine Churchill and suffragette leader Christabel Pankhurst.
Her close friends included Lady Margot Asquith, the widow of the former prime minister Herbert Henry Asquith, Lady Ethel Snowden, the wife of a former Chancellor of the Exchequer, and Lady Londonderry and her husband Charles Vane-Tempest-Stewart, 7th Marquess of Londonderry.