No! Egyptian constitution is based on Islamic law. The principal source of legislation. Egypt is not secular state!
Constitutional Declaration
(Article 1)
The Arab Republic of Egypt is a democratic state based on citizenship. The Egyptian people are part of the Arab nation and work for the realization of its comprehensive unity.
(Article 2)
Islam is the religion of the state and the Arabic language is its official language. Principles of Islamic law (Sharia) are the principal source of legislation.
http://www.cabinet.gov.eg/AboutEgypt/ConstitutionalDeclaration_e.pdf
Modern secularism is a French ideology developed during the French revolution. Became law in 1905.
The queen of UK is the leader of anglicanism.