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Florence was the fourth child and second daughter of Sir Charles Benjamin Bright McLaren, 1st Baron Aberconway and Laura Elizabeth Pochin. Her brothers were the Liberal politicians Henry D McLaren and Francis McLaren. In 1907 she married, as his second wife, Sir Henry Norman, 1st Baronet, a noted journalist and then Liberal MP for Wolverhampton South, who lost this seat in the first election of 1910 but then gained Blackburn in the second election of that year. Amongst the causes Sir Norman helped promote as a politician was women's suffrage of which Lady Norman was herself an active suffragette. She held the post of Hon. Treasurer of the Liberal Women's Suffrage Union. Like her grandparents who started Bodnant Gardens, Florence was a keen horticulturist. When she and her husband acquired Ramster Hall, Surrey she was instrumental in setting out Rhododendrons and Azaleas in the gardens. The gardens were opened to public view under the National Gardens Scheme from 1927 and continue to be opened under that scheme.
After the creation of the Imperial War Museum in 1917 she became chair of one of its subcommittees and was instrumental in ensuring that the contributions of women during the war were recorded and included in the museum's collections. Having an interest in mental health issues, she became the first woman to be appointed to the board of the Royal Earlswood Hospital in 1926. During the Second World War she was a driver for the Women's Voluntary Service in London.
The archives of Lady Norman are held at the Women's Library in London.
- National Portrait Gallery
- Lady Norman riding her Autoped (electric scooter) 1916 
- Lives of the First World War 
- Imperial War Museums records 
- Patrick French, ‘Norman, Sir Henry, first baronet (1858–1939)’, Oxford Dictionary of National Biography, Oxford University Press, 2004; online edn, Jan 2011 accessed 20 June 2017
- Papers of Lady Florence Priscilla Norman
- "Papers of Lady Florence Priscilla Norman - Archives Hub". Retrieved 2017-06-20.