Mill played a crucial, but inflated, role in liberalism. Rothbard did not like Mill much. Mill was a disaster on economic freedom and international issues. Mill rejected that workers and capitalists shared interests. Mill was anti-capitalist.
Mill’s On Liberty addresses the nature and limits of legitimate power by society over individuals. Mill’s relationship with Harriet Taylor, a married woman, twisted his own mores. Mill’s liberalism had little regard for the past. John Maynard Keynes also contributed to liberalism meaning almost anything including Nazism. Keynes felt his system was more adapted to socialism and Stalinism.
But the hallmark of liberalism is that society can run itself with voluntary agreements based upon private property rights.
French liberalism involved the idea of class conflict which led to totalitarianism. This doctrine is generally associated with Marxism, but predated Marx. The French made all government offices open to all citizens. That was the essence of the French Revolution. Two main conflicting classes are producers and plunderers.
The British tradition of liberalism, as Hayek espoused, leaves out the tradition of natural rights.
Lecture 3 of 10 from Ralph Raico's History: The Struggle for Liberty.