P.J. Vatikiotis' History of Modern Egypt is an excellent single volume edition. The most comprehensive coverage of the politics of the era that I'm familiar with are Gershoni and Janikowski's books on the subject, namely "Egypt, Islam and the Arabs: The Search for Egyptian Nationhood, 1900-1930" and "Redefining the Egyptian Nation, 1930-1945."

Referring to this time period as a liberal age comes from Albert Hourani's "Arabic Thought in the Liberal Age 1798-1939" although he obviously puts the end date earlier than you have.

For something of a contrary view Richard P. Mitchell's "The Society of Muslim Brothers" covering the history of the Muslim Brotherhood from it's founding to the early 1950's includes a huge amount of background information on Egypt's political history. I used it extensively for background on my thesis, it's easily the best early history of the Brotherhood I've come across, despite its age.

To add on the excellent reading list here, Re-Envisioning Egypt 1919-1952 is an excellent anthology edited by Arthur Goldschmidt and Amy J. Johnson that covers multiple aspects of the Liberal period. If you want to go away from elite-centered histories, Ordinary Egyptians: Creating the Modern Nation through Popular Culture by Ziad Fahmy is a well-reviewed account that examines Egyptian nationalism through the lens of popular culture.

Finally, in addition to other Gershoni and Janikowski texts, their Confronting Fascism in Egypt: Dictatorship versus Democracy in the 1930s is an important book in that it counters a popular misconception in the West that Egyptians and other Arabs were pro-fascist.